Solver capabilities

• Currently, the supported Result types are:
  • Array
  • Integrals
  • Matrices
  • Generic
  • Concrete
  • Relationals
  • Equation
  • System of Equations
  • Limits
  • Function
  • Derivatives
  • Elementary
  • Numericals

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• Each Result contains a plethora of relevant subsections such as
  • Graphs
  • Numerical Results
  • Simplifications
  • Factorizations
  • Alternate Forms etc

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• The subsections that are returned correspond to the query type.
  Querying a Matrix would give you
  • Determinants
  • Eigenvectors
  • Eigenvalues
  • Inverses etc

Array

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• Input
  $$\{\begin{array}{ll}x& x\ge 0\\ (e^x-1)& x<0\end{array}$$$$\left\{\begin{array}{l}x\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}x\ge 0\\ \left(e^x-1\right)\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}x<0\end{array}\right.$${[x,x >= 0],[(e^(x)-1),x < 0]:}\left\{\begin{array}{ll} x & x \geq 0 \\ \left(e^{x}-1\right) & x<0 \end{array}\right.$$\{\begin{array}{ll}x& x\ge 0\\ (e^x-1)& x<0\end{array}$$

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  • Graph
    

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Integrals

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• Input
  $$\int \frac{x^4+7}{x^3+5x}dx$$$$\int \frac{x^4+7}{x^3+5x}dx$$int(x^(4)+7)/(x^(3)+5x)dx\int \frac{x^{4}+7}{x^{3}+5 x} d x$$\int \frac{x^4+7}{x^3+5x}dx$$

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  • Result
  $$\frac{x^2}{2}+\frac{7\ln \left(x\right)}{5}-\frac{16\ln (x^2+5)}{5}$$$$\frac{x^2}{2}+\frac{7\ln \left(x\right)}{5}-\frac{16\ln \left(x^2+5\right)}{5}$$(x^(2))/(2)+(7ln ((x)))/(5)-(16 ln ((x^(2)+5)))/(5)\frac{x^{2}}{2} + \frac{7 \ln{\left(x \right)}}{5} - \frac{16 \ln{\left(x^{2} + 5 \right)}}{5}$$\frac{x^2}{2}+\frac{7\ln \left(x\right)}{5}-\frac{16\ln (x^2+5)}{5}$$

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  • Simplification
  $$\int \frac{x^4+7}{x(x^2+5)}dx$$$$\int \frac{x^4+7}{x\left(x^2+5\right)}dx$$int(x^(4)+7)/(x(x^(2)+5))dx\int \frac{x^{4} + 7}{x \left(x^{2} + 5\right)}\, dx$$\int \frac{x^4+7}{x(x^2+5)}dx$$

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• Input
  $${\int }_0^1{x}^{2}dx$$$${\int }_0^1 x^{2}dx$$int_(0)^(1)x^(2)dx\int_0^1 x^2 dx$${\int }_0^1{x}^{2}dx$$

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  • Result
  $$\frac{1}{3}$$$$\frac{1}{3}$$(1)/(3)\frac{1}{3}$$\frac{1}{3}$$

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• Input
  $$\int x^2{e}^{-2x}dx$$$$\int x^2{e}^{-2x}dx$$intx^(2)e^(-2x)dx\int x^{2} e^{-2 x} d x$$\int x^2{e}^{-2x}dx$$

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  • Result
  $$\frac{(-2x^2-2x-1)e^{-2x}}{4}$$$$\frac{\left(-2x^2-2x-1\right)e^{-2x}}{4}$$((-2x^(2)-2x-1)e^(-2x))/(4)\frac{\left(- 2 x^{2} - 2 x - 1\right) e^{- 2 x}}{4}$$\frac{(-2x^2-2x-1)e^{-2x}}{4}$$

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• Input
  $$\int 8x{e}^{7x}dx$$$$\int 8x{e}^{7x}dx$$int8xe^(7x)dx\int 8 x e^{7 x} d x$$\int 8x{e}^{7x}dx$$

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  • Result
  $$\frac{(56x-8)e^{7x}}{49}$$$$\frac{\left(56x-8\right)e^{7x}}{49}$$((56 x-8)e^(7x))/(49)\frac{\left(56 x - 8\right) e^{7 x}}{49}$$\frac{(56x-8)e^{7x}}{49}$$

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  • Simplification
  $$\frac{8(7x-1)e^{7x}}{49}$$$$\frac{8\left(7x-1\right)e^{7x}}{49}$$(8(7x-1)e^(7x))/(49)\frac{8 \left(7 x - 1\right) e^{7 x}}{49}$$\frac{8(7x-1)e^{7x}}{49}$$

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• Input
  $$\int \frac{x-3}{(x-1)(x-2)}dx$$$$\int \frac{x-3}{(x-1)(x-2)}dx$$int(x-3)/((x-1)(x-2))dx\int \frac{x-3}{(x-1)(x-2)} d x$$\int \frac{x-3}{(x-1)(x-2)}dx$$

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  • Result
  $$-\ln (x-2)+2\ln (x-1)$$$$-\ln \left(x-2\right)+2\ln \left(x-1\right)$$-ln (x-2)+2ln (x-1)- \ln{\left(x - 2 \right)} + 2 \ln{\left(x - 1 \right)}$$-\ln (x-2)+2\ln (x-1)$$

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  • Simplification
  $$\int \frac{x-3}{(x-2)(x-1)}dx$$$$\int \frac{x-3}{\left(x-2\right)\left(x-1\right)}dx$$int(x-3)/((x-2)(x-1))dx\int \frac{x - 3}{\left(x - 2\right) \left(x - 1\right)}\, dx$$\int \frac{x-3}{(x-2)(x-1)}dx$$

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• Input
  $$\int \frac{x}{\sqrt{2-x^2}}dx$$$$\int \frac{x}{\sqrt{2-x^2}}dx$$int(x)/(sqrt(2-x^(2)))dx\int \frac{x}{\sqrt{2-x^{2}}} d x$$\int \frac{x}{\sqrt{2-x^2}}dx$$

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  • Result
  $$-\sqrt{2-x^2}$$$$-\sqrt{2-x^2}$$-sqrt(2-x^(2))- \sqrt{2 - x^{2}}$$-\sqrt{2-x^2}$$

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  • Simplification
  $$\int \frac{x}{\sqrt{2-x^2}}dx$$$$\int \frac{x}{\sqrt{2-x^2}}dx$$int(x)/(sqrt(2-x^(2)))dx\int \frac{x}{\sqrt{2 - x^{2}}}\, dx$$\int \frac{x}{\sqrt{2-x^2}}dx$$

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• Input
  $$\int e^x\cos 4xdx$$$$\int e^x\cos 4xdx$$inte^(x)cos 4xdx\int e^{x} \cos 4 x d x$$\int e^x\cos 4xdx$$

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  • Result
  $$\frac{4e^x\sin \left(4x\right)}{17}+\frac{e^x\cos \left(4x\right)}{17}$$$$\frac{4e^x\sin \left(4x\right)}{17}+\frac{e^x\cos \left(4x\right)}{17}$$(4e^(x)sin ((4x)))/(17)+(e^(x)cos ((4x)))/(17)\frac{4 e^{x} \sin{\left(4 x \right)}}{17} + \frac{e^{x} \cos{\left(4 x \right)}}{17}$$\frac{4e^x\sin \left(4x\right)}{17}+\frac{e^x\cos \left(4x\right)}{17}$$

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• Input
  $${\int }_0^1{\int }_0^{1-x^2}{\int }_3^{4-x^2-y}xdzdydx$$$${\int }_0^1 {\int }_0^{1-x^2} {\int }_3^{4-x^2-y} xdzdydx$$int_(0)^(1)int_(0)^(1-x^(2))int_(3)^(4-x^(2)-y)xdzdydx\int_{0}^{1} \int_{0}^{1-x^{2}} \int_{3}^{4-x^{2}-y} x d z d y d x$${\int }_0^1{\int }_0^{1-x^2}{\int }_3^{4-x^2-y}xdzdydx$$

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  • Result
  $$\frac{1}{12}$$$$\frac{1}{12}$$(1)/(12)\frac{1}{12}$$\frac{1}{12}$$

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  • Simplification
  $$\underset{0}{\overset{1}{\int }}\underset{0}{\overset{1-x^2}{\int }}\underset{3}{\overset{-x^2-y+4}{\int }}xdzdydx$$$$\underset{0}{\overset{1}{\int }} \underset{0}{\overset{1-x^2}{\int }} \underset{3}{\overset{-x^2-y+4}{\int }} xdzdydx$$int_(0)^(1)int_(0)^(1-x^(2))int_(3)^(-x^(2)-y+4)xdzdydx\int\limits_{0}^{1}\int\limits_{0}^{1 - x^{2}}\int\limits_{3}^{- x^{2} - y + 4} x\, dz\, dy\, dx$$\underset{0}{\overset{1}{\int }}\underset{0}{\overset{1-x^2}{\int }}\underset{3}{\overset{-x^2-y+4}{\int }}xdzdydx$$

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• Input
  $$\int \frac{e^x}{1+e^{2x}}dx=$$$$\int \frac{e^x}{1+e^{2x}}dx=$$int(e^(x))/(1+e^(2x))dx=\int \frac{e^{x}}{1+e^{2 x}} d x=$$\int \frac{e^x}{1+e^{2x}}dx=$$

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  • Result
  $${\tan }^{-1}\left(e^x\right)$$$${\tan }^{-1}\left(e^x\right)$$tan^(-1)(e^(x))\tan^{-1}{\left(e^{x} \right)}$${\tan }^{-1}\left(e^x\right)$$

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  • Simplification
  $$\int \frac{1}{2\cosh \left(x\right)}dx$$$$\int \frac{1}{2\cosh \left(x\right)}dx$$int(1)/(2cosh ((x)))dx\int \frac{1}{2 \cosh{\left(x \right)}}\, dx$$\int \frac{1}{2\cosh \left(x\right)}dx$$

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• Input
  $$\int (\frac{4}{3y}+\frac{3}{y^2}-\frac{2}{\sqrt[7]{y}})dy$$$$\int \left(\frac{4}{3y}+\frac{3}{y^2}-\frac{2}{\sqrt[7]{y}}\right)dy$$int((4)/(3y)+(3)/(y^(2))-(2)/(root(7)(y)))dy\int\left(\frac{4}{3 y}+\frac{3}{y^{2}}-\frac{2}{\sqrt[7]{y}}\right) d y$$\int (\frac{4}{3y}+\frac{3}{y^2}-\frac{2}{\sqrt[7]{y}})dy$$

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  • Result
  $$-\frac{7y^{\frac{6}{7}}}{3}+\frac{4\ln \left(y\right)}{3}-\frac{3}{y}$$$$-\frac{7y^{\frac{6}{7}}}{3}+\frac{4\ln \left(y\right)}{3}-\frac{3}{y}$$-(7y^((6)/(7)))/(3)+(4ln ((y)))/(3)-(3)/(y)- \frac{7 y^{\frac{6}{7}}}{3} + \frac{4 \ln{\left(y \right)}}{3} - \frac{3}{y}$$-\frac{7y^{\frac{6}{7}}}{3}+\frac{4\ln \left(y\right)}{3}-\frac{3}{y}$$

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  • Simplification
  $$\int (\frac{4}{3y}+\frac{3}{y^2}-\frac{2}{\sqrt[7]{y}})dy$$$$\int \left(\frac{4}{3y}+\frac{3}{y^2}-\frac{2}{\sqrt[7]{y}}\right)dy$$int((4)/(3y)+(3)/(y^(2))-(2)/(root(7)(y)))dy\int \left(\frac{4}{3 y} + \frac{3}{y^{2}} - \frac{2}{\sqrt[7]{y}}\right)\, dy$$\int (\frac{4}{3y}+\frac{3}{y^2}-\frac{2}{\sqrt[7]{y}})dy$$

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• Input
  $${\int }_1^{5}1+\frac{1}{u}+\frac{1}{u^2}du$$$${\int }_1^5 1+\frac{1}{u}+\frac{1}{u^2}du$$int_(1)^(5)1+(1)/(u)+(1)/(u^(2))du\int_{1}^{5} 1+\frac{1}{u}+\frac{1}{u^{2}} d u$${\int }_1^{5}1+\frac{1}{u}+\frac{1}{u^2}du$$

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  • Result
  $$\ln \left(5\right)+\frac{24}{5}$$$$\ln \left(5\right)+\frac{24}{5}$$ln (5)+(24)/(5)\ln{\left(5 \right)} + \frac{24}{5}$$\ln \left(5\right)+\frac{24}{5}$$

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• Input
  $$\int (-8e^t+19t)dt$$$$\int \left(-8e^t+19t\right)dt$$int(-8e^(t)+19 t)dt\int\left(-8 e^{t}+19 t\right) d t$$\int (-8e^t+19t)dt$$

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  • Result
  $$\frac{19t^2}{2}-8e^t$$$$\frac{19t^2}{2}-8e^t$$(19t^(2))/(2)-8e^(t)\frac{19 t^{2}}{2} - 8 e^{t}$$\frac{19t^2}{2}-8e^t$$

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• Input
  $$\int e^{3x+9}dx$$$$\int e^{3x+9}dx$$inte^(3x+9)dx\int e^{3 x+9} d x$$\int e^{3x+9}dx$$

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  • Result
  $$\frac{e^{3x+9}}{3}$$$$\frac{e^{3x+9}}{3}$$(e^(3x+9))/(3)\frac{e^{3 x + 9}}{3}$$\frac{e^{3x+9}}{3}$$

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Matrices

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• Input
  $$\left[\begin{array}{cc}-1& 7\\ 3& 7\end{array}\right]\left[\begin{array}{rr}-1& 7\\ 3& 7\end{array}\right]$$$$\left[\begin{array}{cc}-1& 7\\ 3& 7\end{array}\right]\left[\begin{array}{r}-1\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}7\\ 3\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}7\end{array}\right]$$[[-1,7],[3,7]][[-1,7],[3,7]]\left[\begin{array}{cc}-1 & 7 \\ 3 & 7\end{array}\right]\left[\begin{array}{rr}-1 & 7 \\ 3 & 7\end{array}\right]$$\left[\begin{array}{cc}-1& 7\\ 3& 7\end{array}\right]\left[\begin{array}{rr}-1& 7\\ 3& 7\end{array}\right]$$

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  • Result
  $$\left[\begin{array}{cc}22& 42\\ 18& 70\end{array}\right]$$$$\left[\begin{array}{cc}22& 42\\ 18& 70\end{array}\right]$$[[22,42],[18,70]]\left[\begin{matrix}22 & 42\\18 & 70\end{matrix}\right]$$\left[\begin{array}{cc}22& 42\\ 18& 70\end{array}\right]$$

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  • Inverse
  $$\left[\begin{array}{cc}\frac{5}{56}& -\frac{3}{56}\\ -\frac{9}{392}& \frac{11}{392}\end{array}\right]$$$$\left[\begin{array}{cc}\frac{5}{56}& -\frac{3}{56}\\ -\frac{9}{392}& \frac{11}{392}\end{array}\right]$$[[(5)/(56),-(3)/(56)],[-(9)/(392),(11)/(392)]]\left[\begin{matrix}\frac{5}{56} & - \frac{3}{56}\\- \frac{9}{392} & \frac{11}{392}\end{matrix}\right]$$\left[\begin{array}{cc}\frac{5}{56}& -\frac{3}{56}\\ -\frac{9}{392}& \frac{11}{392}\end{array}\right]$$

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  • Determinant
  $$784$$$$784$$784784$$784$$

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  • Eigenvectors
  $$\{\begin{array}{l}{v}_{{\lambda }_1}=\left[\begin{array}{c}-\frac{42}{-24+6\sqrt{37}}\\ 1\end{array}\right]\\ v_{{\lambda }_2}=\left[\begin{array}{c}-\frac{42}{-6\sqrt{37}-24}\\ 1\end{array}\right]\end{array}$$$$\left\{\begin{array}{l}{v}_{{\lambda }_1}=\left[\begin{array}{c}-\frac{42}{-24+6\sqrt{37}}\\ 1\end{array}\right]\\ v_{{\lambda }_2}=\left[\begin{array}{c}-\frac{42}{-6\sqrt{37}-24}\\ 1\end{array}\right]\end{array}\right.$${[v_(lambda_(1))=[[-(42)/(-24+6sqrt37)],[1]]],[v_(lambda_(2))=[[-(42)/(-6sqrt37-24)],[1]]]:}\left\{ \begin{array} {l} \,v_{\lambda_1}=\left[\begin{matrix}- \frac{42}{-24 + 6 \sqrt{37}}\\1\end{matrix}\right] \\\, v_{\lambda_2}=\left[\begin{matrix}- \frac{42}{- 6 \sqrt{37} - 24}\\1\end{matrix}\right] \end{array} \right.$$\{\begin{array}{l}{v}_{{\lambda }_1}=\left[\begin{array}{c}-\frac{42}{-24+6\sqrt{37}}\\ 1\end{array}\right]\\ v_{{\lambda }_2}=\left[\begin{array}{c}-\frac{42}{-6\sqrt{37}-24}\\ 1\end{array}\right]\end{array}$$

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  • Eigenvalues
  $$\{\begin{array}{l}{\lambda }_1=46-6\sqrt{37}\\ {\lambda }_2=6\sqrt{37}+46\end{array}$$$$\left\{\begin{array}{l}{\lambda }_1=46-6\sqrt{37}\\ {\lambda }_2=6\sqrt{37}+46\end{array}\right.$${[lambda_(1)=46-6sqrt37],[lambda_(2)=6sqrt37+46]:}\left\{ \begin{array} {l} \,\lambda_1=46 - 6 \sqrt{37} \\\, \lambda_2=6 \sqrt{37} + 46 \end{array} \right.$$\{\begin{array}{l}{\lambda }_1=46-6\sqrt{37}\\ {\lambda }_2=6\sqrt{37}+46\end{array}$$

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  • Characteristic Polynomial
  $$p\left(\lambda \right)={\lambda }^2-92\lambda +784$$$$p\left(\lambda \right)={\lambda }^2-92\lambda +784$$p(lambda)=lambda^(2)-92 lambda+784p{\left(\lambda \right)} = \lambda^{2} - 92 \lambda + 784$$p\left(\lambda \right)={\lambda }^2-92\lambda +784$$

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  • Dimensions
  $$(2,2)$$$$\left(2,2\right)$$(2,2)\left( 2, \ 2\right)$$(2,2)$$

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  • Multiplicities
  $$\{\begin{array}{l}{\mu }_A({\lambda }_1)=1\\ {\mu }_A({\lambda }_2)=1\end{array}$$$$\left\{\begin{array}{l}{\mu }_A({\lambda }_1)=1\\ {\mu }_A({\lambda }_2)=1\end{array}\right.$${[mu _(A)(lambda_(1))=1],[mu _(A)(lambda_(2))=1]:}\left\{ \begin{array} {l} \,\mu_A(\lambda_1)=1 \\\, \mu_A(\lambda_2)=1 \end{array} \right.$$\{\begin{array}{l}{\mu }_A({\lambda }_1)=1\\ {\mu }_A({\lambda }_2)=1\end{array}$$

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• Input
  $$\left[\begin{array}{rrr}-3& -5& -3\\ 1& 3& 5\end{array}\right]+\left[\begin{array}{rrr}3& 1& 0\\ -2& 6& -2\end{array}\right]$$$$\left[\begin{array}{r}-3\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}-5\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}-3\\ 1\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}3\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}5\end{array}\right]+\left[\begin{array}{r}3\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}1\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}0\\ -2\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}6\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}-2\end{array}\right]$$[[-3,-5,-3],[1,3,5]]+[[3,1,0],[-2,6,-2]]\left[\begin{array}{rrr}-3 & -5 & -3 \\ 1 & 3 & 5\end{array}\right]+\left[\begin{array}{rrr}3 & 1 & 0 \\ -2 & 6 & -2\end{array}\right]$$\left[\begin{array}{rrr}-3& -5& -3\\ 1& 3& 5\end{array}\right]+\left[\begin{array}{rrr}3& 1& 0\\ -2& 6& -2\end{array}\right]$$

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  • Result
  $$\left[\begin{array}{ccc}0& -4& -3\\ -1& 9& 3\end{array}\right]$$$$\left[\begin{array}{ccc}0& -4& -3\\ -1& 9& 3\end{array}\right]$$[[0,-4,-3],[-1,9,3]]\left[\begin{matrix}0 & -4 & -3\\-1 & 9 & 3\end{matrix}\right]$$\left[\begin{array}{ccc}0& -4& -3\\ -1& 9& 3\end{array}\right]$$

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• Input
  $$\left[\begin{array}{cc}4& -5\\ -6& 5\\ -1& 4\end{array}\right]-\left[\begin{array}{cc}2& -4\\ -6& 2\\ 3& -1\end{array}\right]$$$$\left[\begin{array}{cc}4& -5\\ -6& 5\\ -1& 4\end{array}\right]-\left[\begin{array}{cc}2& -4\\ -6& 2\\ 3& -1\end{array}\right]$$[[4,-5],[-6,5],[-1,4]]-[[2,-4],[-6,2],[3,-1]]\left[\begin{array}{cc}4 & -5 \\ -6 & 5 \\ -1 & 4\end{array}\right]-\left[\begin{array}{cc}2 & -4 \\ -6 & 2 \\ 3 & -1\end{array}\right]$$\left[\begin{array}{cc}4& -5\\ -6& 5\\ -1& 4\end{array}\right]-\left[\begin{array}{cc}2& -4\\ -6& 2\\ 3& -1\end{array}\right]$$

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  • Result
  $$\left[\begin{array}{cc}2& -1\\ 0& 3\\ -4& 5\end{array}\right]$$$$\left[\begin{array}{cc}2& -1\\ 0& 3\\ -4& 5\end{array}\right]$$[[2,-1],[0,3],[-4,5]]\left[\begin{matrix}2 & -1\\0 & 3\\-4 & 5\end{matrix}\right]$$\left[\begin{array}{cc}2& -1\\ 0& 3\\ -4& 5\end{array}\right]$$

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• Input
  $$\left(\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right)$$$$\left(\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right)$$([cos theta,sin theta],[-sin theta,cos theta])\left(\begin{array}{cc} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right)$$\left(\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right)$$

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  • Result
  $$\left[\begin{array}{cc}\cos \left(\theta \right)& \sin \left(\theta \right)\\ -\sin \left(\theta \right)& \cos \left(\theta \right)\end{array}\right]$$$$\left[\begin{array}{cc}\cos \left(\theta \right)& \sin \left(\theta \right)\\ -\sin \left(\theta \right)& \cos \left(\theta \right)\end{array}\right]$$[[cos (theta),sin (theta)],[-sin (theta),cos (theta)]]\left[\begin{matrix}\cos{\left(\theta \right)} & \sin{\left(\theta \right)}\\- \sin{\left(\theta \right)} & \cos{\left(\theta \right)}\end{matrix}\right]$$\left[\begin{array}{cc}\cos \left(\theta \right)& \sin \left(\theta \right)\\ -\sin \left(\theta \right)& \cos \left(\theta \right)\end{array}\right]$$

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  • Inverse
  $$\left[\begin{array}{cc}\frac{1-{\sin }^2\left(\theta \right)}{\cos \left(\theta \right)}& -\sin \left(\theta \right)\\ \sin \left(\theta \right)& \cos \left(\theta \right)\end{array}\right]$$$$\left[\begin{array}{cc}\frac{1-{\sin }^2\left(\theta \right)}{\cos \left(\theta \right)}& -\sin \left(\theta \right)\\ \sin \left(\theta \right)& \cos \left(\theta \right)\end{array}\right]$$[[(1-sin^(2)((theta)))/(cos ((theta))),-sin (theta)],[sin (theta),cos (theta)]]\left[\begin{matrix}\frac{1 - \sin^{2}{\left(\theta \right)}}{\cos{\left(\theta \right)}} & - \sin{\left(\theta \right)}\\\sin{\left(\theta \right)} & \cos{\left(\theta \right)}\end{matrix}\right]$$\left[\begin{array}{cc}\frac{1-{\sin }^2\left(\theta \right)}{\cos \left(\theta \right)}& -\sin \left(\theta \right)\\ \sin \left(\theta \right)& \cos \left(\theta \right)\end{array}\right]$$

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  • Determinant
  $${\sin }^2\left(\theta \right)+{\cos }^2\left(\theta \right)$$$${\sin }^2\left(\theta \right)+{\cos }^2\left(\theta \right)$$sin^(2)(theta)+cos^(2)(theta)\sin^{2}{\left(\theta \right)} + \cos^{2}{\left(\theta \right)}$${\sin }^2\left(\theta \right)+{\cos }^2\left(\theta \right)$$

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  • Eigenvectors
  $$\{\begin{array}{l}{v}_{{\lambda }_1}=\left[\begin{array}{c}-\frac{\sin \left(\theta \right)}{\sqrt{(\cos \left(\theta \right)-1)(\cos \left(\theta \right)+1)}}\\ 1\end{array}\right]\\ v_{{\lambda }_2}=\left[\begin{array}{c}\frac{\sin \left(\theta \right)}{\sqrt{(\cos \left(\theta \right)-1)(\cos \left(\theta \right)+1)}}\\ 1\end{array}\right]\end{array}$$$$\left\{\begin{array}{l}{v}_{{\lambda }_1}=\left[\begin{array}{c}-\frac{\sin \left(\theta \right)}{\sqrt{\left(\cos \left(\theta \right)-1\right)\left(\cos \left(\theta \right)+1\right)}}\\ 1\end{array}\right]\\ v_{{\lambda }_2}=\left[\begin{array}{c}\frac{\sin \left(\theta \right)}{\sqrt{\left(\cos \left(\theta \right)-1\right)\left(\cos \left(\theta \right)+1\right)}}\\ 1\end{array}\right]\end{array}\right.$${[v_(lambda_(1))=[[-(sin ((theta)))/(sqrt((cos ((theta))-1)(cos ((theta))+1)))],[1]]],[v_(lambda_(2))=[[(sin ((theta)))/(sqrt((cos ((theta))-1)(cos ((theta))+1)))],[1]]]:}\left\{ \begin{array} {l} \,v_{\lambda_1}=\left[\begin{matrix}- \frac{\sin{\left(\theta \right)}}{\sqrt{\left(\cos{\left(\theta \right)} - 1\right) \left(\cos{\left(\theta \right)} + 1\right)}}\\1\end{matrix}\right] \\\, v_{\lambda_2}=\left[\begin{matrix}\frac{\sin{\left(\theta \right)}}{\sqrt{\left(\cos{\left(\theta \right)} - 1\right) \left(\cos{\left(\theta \right)} + 1\right)}}\\1\end{matrix}\right] \end{array} \right.$$\{\begin{array}{l}{v}_{{\lambda }_1}=\left[\begin{array}{c}-\frac{\sin \left(\theta \right)}{\sqrt{(\cos \left(\theta \right)-1)(\cos \left(\theta \right)+1)}}\\ 1\end{array}\right]\\ v_{{\lambda }_2}=\left[\begin{array}{c}\frac{\sin \left(\theta \right)}{\sqrt{(\cos \left(\theta \right)-1)(\cos \left(\theta \right)+1)}}\\ 1\end{array}\right]\end{array}$$

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  • Eigenvalues
  $$\{\begin{array}{l}{\lambda }_1=-\sqrt{(\cos \left(\theta \right)-1)(\cos \left(\theta \right)+1)}+\cos \left(\theta \right)\\ {\lambda }_2=\sqrt{(\cos \left(\theta \right)-1)(\cos \left(\theta \right)+1)}+\cos \left(\theta \right)\end{array}$$$$\left\{\begin{array}{l}{\lambda }_1=-\sqrt{\left(\cos \left(\theta \right)-1\right)\left(\cos \left(\theta \right)+1\right)}+\cos \left(\theta \right)\\ {\lambda }_2=\sqrt{\left(\cos \left(\theta \right)-1\right)\left(\cos \left(\theta \right)+1\right)}+\cos \left(\theta \right)\end{array}\right.$${[lambda_(1)=-sqrt((cos ((theta))-1)(cos ((theta))+1))+cos (theta)],[lambda_(2)=sqrt((cos ((theta))-1)(cos ((theta))+1))+cos (theta)]:}\left\{ \begin{array} {l} \,\lambda_1=- \sqrt{\left(\cos{\left(\theta \right)} - 1\right) \left(\cos{\left(\theta \right)} + 1\right)} + \cos{\left(\theta \right)} \\\, \lambda_2=\sqrt{\left(\cos{\left(\theta \right)} - 1\right) \left(\cos{\left(\theta \right)} + 1\right)} + \cos{\left(\theta \right)} \end{array} \right.$$\{\begin{array}{l}{\lambda }_1=-\sqrt{(\cos \left(\theta \right)-1)(\cos \left(\theta \right)+1)}+\cos \left(\theta \right)\\ {\lambda }_2=\sqrt{(\cos \left(\theta \right)-1)(\cos \left(\theta \right)+1)}+\cos \left(\theta \right)\end{array}$$

  ---

  • Characteristic Polynomial
  $$p\left(\lambda \right)={\lambda }^2-2\lambda \cos \left(\theta \right)+1$$$$p\left(\lambda \right)={\lambda }^2-2\lambda \cos \left(\theta \right)+1$$p(lambda)=lambda^(2)-2lambda cos (theta)+1p{\left(\lambda \right)} = \lambda^{2} - 2 \lambda \cos{\left(\theta \right)} + 1$$p\left(\lambda \right)={\lambda }^2-2\lambda \cos \left(\theta \right)+1$$

  ---

  • Dimensions
  $$(2,2)$$$$\left(2,2\right)$$(2,2)\left( 2, \ 2\right)$$(2,2)$$

  ---

  • Multiplicities
  $$\{\begin{array}{l}{\mu }_A({\lambda }_1)=1\\ {\mu }_A({\lambda }_2)=1\end{array}$$$$\left\{\begin{array}{l}{\mu }_A({\lambda }_1)=1\\ {\mu }_A({\lambda }_2)=1\end{array}\right.$${[mu _(A)(lambda_(1))=1],[mu _(A)(lambda_(2))=1]:}\left\{ \begin{array} {l} \,\mu_A(\lambda_1)=1 \\\, \mu_A(\lambda_2)=1 \end{array} \right.$$\{\begin{array}{l}{\mu }_A({\lambda }_1)=1\\ {\mu }_A({\lambda }_2)=1\end{array}$$

---

Generic

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• Input
  $${(-18m^{2}n)}^2\ast (-\frac{1}{6}m{n}^2)=$$$${\left(-18m^{2}n\right)}^2\ast \left(-\frac{1}{6}m{n}^2\right)=$$(-18m^(2)n)^(2)**(-(1)/(6)mn^(2))=\left(-18 m^{2} n\right)^{2} *\left(-\frac{1}{6} m n^{2}\right)=$${(-18m^{2}n)}^2\ast (-\frac{1}{6}m{n}^2)=$$

  ---

  • Roots
  $$\{\begin{array}{l}m=0\\ n=0\end{array}$$$$\left\{\begin{array}{l}m=0\\ n=0\end{array}\right.$${[m=0],[n=0]:}\left\{ \begin{array} {l} \,m = 0 \\\, n = 0 \end{array} \right.$$\{\begin{array}{l}m=0\\ n=0\end{array}$$

  ---

  • Result
  $$-54m^5{n}^4$$$$-54m^5{n}^4$$-54m^(5)n^(4)- 54 m^{5} n^{4}$$-54m^5{n}^4$$

  ---

  • Graph
    

---

• Input
  $${\log }_6\frac{1}{6}$$$${\log }_6\frac{1}{6}$$log_(6)((1)/(6))\log _{6} \frac{1}{6}$${\log }_6\frac{1}{6}$$

  ---

  • Result
  $$-1$$$$-1$$-1-1$$-1$$

---

• Input
  $$(-7+6i)(3+i)$$$$(-7+6i)(3+i)$$(-7+6i)(3+i)(-7+6 i)(3+i)$$(-7+6i)(3+i)$$

  ---

  • Result
  $$(-7+6i)(3+i)$$$$\left(-7+6i\right)\left(3+i\right)$$(-7+6i)(3+i)\left(-7 + 6 i\right) \left(3 + i\right)$$(-7+6i)(3+i)$$

  ---

  • Numerical
  $$-27.0+11.0i$$$$-27.0+11.0i$$-27.0+11.0 i-27.0 + 11.0 i$$-27.0+11.0i$$

  ---

  • Simplification
  $$-27+11i$$$$-27+11i$$-27+11 i-27 + 11 i$$-27+11i$$

---

• Input
  $$\sqrt{\frac{252q^6{k}^{16}}{175q{k}^4}}$$$$\sqrt{\frac{252q^6{k}^{16}}{175q{k}^4}}$$sqrt((252q^(6)k^(16))/(175 qk^(4)))\sqrt{\frac{252 q^{6} k^{16}}{175 q k^{4}}}$$\sqrt{\frac{252q^6{k}^{16}}{175q{k}^4}}$$

  ---

  • Result
  $$\frac{6\sqrt{k^{12}{q}^5}}{5}$$$$\frac{6\sqrt{k^{12}{q}^5}}{5}$$(6sqrt(k^(12)q^(5)))/(5)\frac{6 \sqrt{k^{12} q^{5}}}{5}$$\frac{6\sqrt{k^{12}{q}^5}}{5}$$

  ---

  • Expansion
  $$6\sqrt{7}\frac{\sqrt{7}\sqrt{k^{12}{q}^5}}{35}$$$$6\sqrt{7}\frac{\sqrt{7}\sqrt{k^{12}{q}^5}}{35}$$6sqrt7(sqrt7sqrt(k^(12)q^(5)))/(35)6 \sqrt{7} \frac{\sqrt{7} \sqrt{k^{12} q^{5}}}{35}$$6\sqrt{7}\frac{\sqrt{7}\sqrt{k^{12}{q}^5}}{35}$$

  ---

  • Graph
    

---

• Input
  $$\frac{\sqrt{160y^{10}}}{\sqrt{2y^2}}$$$$\frac{\sqrt{160y^{10}}}{\sqrt{2y^2}}$$(sqrt(160y^(10)))/(sqrt(2y^(2)))\frac{\sqrt{160 y^{10}}}{\sqrt{2 y^{2}}}$$\frac{\sqrt{160y^{10}}}{\sqrt{2y^2}}$$

  ---

  • Result
  $$\frac{4\sqrt{5}\sqrt{y^{10}}}{\sqrt{y^2}}$$$$\frac{4\sqrt{5}\sqrt{y^{10}}}{\sqrt{y^2}}$$(4sqrt5sqrt(y^(10)))/(sqrt(y^(2)))\frac{4 \sqrt{5} \sqrt{y^{10}}}{\sqrt{y^{2}}}$$\frac{4\sqrt{5}\sqrt{y^{10}}}{\sqrt{y^2}}$$

  ---

  • Graph
    

---

• Input
  $$\frac{z}{z^2+9z+14}+\frac{2}{z^2+9z+14}$$$$\frac{z}{z^2+9z+14}+\frac{2}{z^2+9z+14}$$(z)/(z^(2)+9z+14)+(2)/(z^(2)+9z+14)\frac{z}{z^{2}+9 z+14}+\frac{2}{z^{2}+9 z+14}$$\frac{z}{z^2+9z+14}+\frac{2}{z^2+9z+14}$$

  ---

  • Result
  $$\frac{z}{z^2+9z+14}+\frac{2}{z^2+9z+14}$$$$\frac{z}{z^2+9z+14}+\frac{2}{z^2+9z+14}$$(z)/(z^(2)+9z+14)+(2)/(z^(2)+9z+14)\frac{z}{z^{2} + 9 z + 14} + \frac{2}{z^{2} + 9 z + 14}$$\frac{z}{z^2+9z+14}+\frac{2}{z^2+9z+14}$$

  ---

  • Simplification
  $$\frac{1}{z+7}$$$$\frac{1}{z+7}$$(1)/(z+7)\frac{1}{z + 7}$$\frac{1}{z+7}$$

  ---

  • Expansion
  $$\frac{z}{(z^2+9z)+14}+\frac{2}{(z^2+9z)+14}$$$$\frac{z}{\left(z^2+9z\right)+14}+\frac{2}{\left(z^2+9z\right)+14}$$(z)/((z^(2)+9z)+14)+(2)/((z^(2)+9z)+14)\frac{z}{\left(z^{2} + 9 z\right) + 14} + \frac{2}{\left(z^{2} + 9 z\right) + 14}$$\frac{z}{(z^2+9z)+14}+\frac{2}{(z^2+9z)+14}$$

  ---

  • Graph
    

---

• Input
  $$\frac{14!}{(14-4)!}$$$$\frac{14!}{(14-4)!}$$(14!)/((14-4)!)\frac{14 !}{(14-4) !}$$\frac{14!}{(14-4)!}$$

  ---

  • Factorization
  $$\frac{14!}{(-4+14)!}$$$$\frac{14!}{\left(-4+14\right)!}$$(14!)/((-4+14)!)\frac{14!}{\left(-4 + 14\right)!}$$\frac{14!}{(-4+14)!}$$

  ---

  • Result
  $$24024$$$$24024$$2402424024$$24024$$

---

• Input
  $$(5-9i)(5+9i)$$$$(5-9i)(5+9i)$$(5-9i)(5+9i)(5-9 i)(5+9 i)$$(5-9i)(5+9i)$$

  ---

  • Result
  $$(5-9i)(5+9i)$$$$\left(5-9i\right)\left(5+9i\right)$$(5-9i)(5+9i)\left(5 - 9 i\right) \left(5 + 9 i\right)$$(5-9i)(5+9i)$$

  ---

  • Numerical
  $$106.0$$$$106.0$$106.0106.0$$106.0$$

  ---

  • Simplification
  $$106$$$$106$$106106$$106$$

---

• Input
  $$125x^3-216m^3$$$$125x^3-216m^3$$125x^(3)-216m^(3)125 x^{3}-216 m^{3}$$125x^3-216m^3$$

  ---

  • Factorization
  $$(-6m+5x)(36m^2+30mx+25x^2)$$$$\left(-6m+5x\right)\left(36m^2+30mx+25x^2\right)$$(-6m+5x)(36m^(2)+30 mx+25x^(2))\left(- 6 m + 5 x\right) \left(36 m^{2} + 30 m x + 25 x^{2}\right)$$(-6m+5x)(36m^2+30mx+25x^2)$$

  ---

  • Roots
  $$\{\begin{array}{l}m=\frac{5x}{6},m=x(-\frac{5}{12}-\frac{5\sqrt{3}i}{12}),m=x(-\frac{5}{12}+\frac{5\sqrt{3}i}{12})\\ x=\frac{6m}{5},x=6m(-\frac{1}{10}-\frac{\sqrt{3}i}{10}),x=6m(-\frac{1}{10}+\frac{\sqrt{3}i}{10})\end{array}$$$$\left\{\begin{array}{l}m=\frac{5x}{6},m=x\left(-\frac{5}{12}-\frac{5\sqrt{3}i}{12}\right),m=x\left(-\frac{5}{12}+\frac{5\sqrt{3}i}{12}\right)\\ x=\frac{6m}{5},x=6m\left(-\frac{1}{10}-\frac{\sqrt{3}i}{10}\right),x=6m\left(-\frac{1}{10}+\frac{\sqrt{3}i}{10}\right)\end{array}\right.$${[m=(5x)/(6)","quad m=x(-(5)/(12)-(5sqrt3i)/(12))","quad m=x(-(5)/(12)+(5sqrt3i)/(12))],[x=(6m)/(5)","quad x=6m(-(1)/(10)-(sqrt3i)/(10))","quad x=6m(-(1)/(10)+(sqrt3i)/(10))]:}\left\{ \begin{array} {l} \,m = \frac{5 x}{6}\,,\quad m = x \left(- \frac{5}{12} - \frac{5 \sqrt{3} i}{12}\right)\,,\quad m = x \left(- \frac{5}{12} + \frac{5 \sqrt{3} i}{12}\right) \\\, x = \frac{6 m}{5}\,,\quad x = 6 m \left(- \frac{1}{10} - \frac{\sqrt{3} i}{10}\right)\,,\quad x = 6 m \left(- \frac{1}{10} + \frac{\sqrt{3} i}{10}\right) \end{array} \right.$$\{\begin{array}{l}m=\frac{5x}{6},m=x(-\frac{5}{12}-\frac{5\sqrt{3}i}{12}),m=x(-\frac{5}{12}+\frac{5\sqrt{3}i}{12})\\ x=\frac{6m}{5},x=6m(-\frac{1}{10}-\frac{\sqrt{3}i}{10}),x=6m(-\frac{1}{10}+\frac{\sqrt{3}i}{10})\end{array}$$

  ---

  • Result
  $$-216m^3+125x^3$$$$-216m^3+125x^3$$-216m^(3)+125x^(3)- 216 m^{3} + 125 x^{3}$$-216m^3+125x^3$$

  ---

  • Graph
    

---

• Input
  $$(5+2i{)}^2$$$$(5+2i{)}^2$$(5+2i)^(2)(5+2 i)^{2}$$(5+2i{)}^2$$

  ---

  • Result
  $${(5+2i)}^2$$$${\left(5+2i\right)}^2$$(5+2i)^(2)\left(5 + 2 i\right)^{2}$${(5+2i)}^2$$

  ---

  • Numerical
  $$21.0+20.0i$$$$21.0+20.0i$$21.0+20.0 i21.0 + 20.0 i$$21.0+20.0i$$

  ---

  • Simplification
  $$21+20i$$$$21+20i$$21+20 i21 + 20 i$$21+20i$$

---

• Input
  $$x^2+3x-18$$$$x^2+3x-18$$x^(2)+3x-18x^{2}+3 x-18$$x^2+3x-18$$

  ---

  • Factorization
  $$(x-3)(x+6)$$$$\left(x-3\right)\left(x+6\right)$$(x-3)(x+6)\left(x - 3\right) \left(x + 6\right)$$(x-3)(x+6)$$

  ---

  • Roots
  $$x\in \{-6,3\}$$$$x\in \left\{-6,3\right\}$$x in{-6,3}x \in \left\{ -6,\, 3\right\}$$x\in \{-6,3\}$$

  ---

  • Result
  $$x^2+3x-18$$$$x^2+3x-18$$x^(2)+3x-18x^{2} + 3 x - 18$$x^2+3x-18$$

  ---

  • Expansion
  $$(x^2+3x)-18$$$$\left(x^2+3x\right)-18$$(x^(2)+3x)-18\left(x^{2} + 3 x\right) - 18$$(x^2+3x)-18$$

  ---

  • Graph
    

---

• Input
  $$2{\cos }^2\left({44}^{\circ }\right)-1$$$$2{\cos }^2\left({44}^{\circ }\right)-1$$2cos^(2)(44^(@))-12 \cos ^{2}\left(44^{\circ}\right)-1$$2{\cos }^2\left({44}^{\circ }\right)-1$$

  ---

  • Result
  $$-1+2{\cos }^2\left(\frac{11\pi }{45}\right)$$$$-1+2{\cos }^2\left(\frac{11\pi }{45}\right)$$-1+2cos^(2)((11 pi)/(45))-1 + 2 \cos^{2}{\left(\frac{11 \pi}{45} \right)}$$-1+2{\cos }^2\left(\frac{11\pi }{45}\right)$$

  ---

  • Numerical
  $$0.034899496702501$$$$0.034899496702501$$0.0348994967025010.034899496702501$$0.034899496702501$$

  ---

  • Simplification
  $$\cos \left(\frac{22\pi }{45}\right)$$$$\cos \left(\frac{22\pi }{45}\right)$$cos ((22 pi)/(45))\cos{\left(\frac{22 \pi}{45} \right)}$$\cos \left(\frac{22\pi }{45}\right)$$

---

• Input
  $$(-18)÷6\times (-12)=$$$$(-18)÷6\times (-12)=$$(-18)-:6xx(-12)=(-18) \div 6 \times(-12)=$$(-18)÷6\times (-12)=$$

  ---

  • Result
  $$36$$$$36$$3636$$36$$

---

• Input
  $$\ln \left(\frac{e^5}{6}\right)$$$$\ln \left(\frac{e^5}{6}\right)$$ln((e^(5))/(6))\ln \left(\frac{e^{5}}{6}\right)$$\ln \left(\frac{e^5}{6}\right)$$

  ---

  • Result
  $$\ln \left(\frac{e^5}{6}\right)$$$$\ln \left(\frac{e^5}{6}\right)$$ln ((e^(5))/(6))\ln{\left(\frac{e^{5}}{6} \right)}$$\ln \left(\frac{e^5}{6}\right)$$

  ---

  • Numerical
  $$3.20824053077195$$$$3.20824053077195$$3.208240530771953.20824053077195$$3.20824053077195$$

  ---

  • Simplification
  $$5-\ln \left(6\right)$$$$5-\ln \left(6\right)$$5-ln (6)5 - \ln{\left(6 \right)}$$5-\ln \left(6\right)$$

---

• Input
  $$a^2+b^2+2ab$$$$a^2+b^2+2ab$$a^(2)+b^(2)+2aba^2 + b^2 + 2 a b$$a^2+b^2+2ab$$

  ---

  • Factorization
  $${(a+b)}^2$$$${\left(a+b\right)}^2$$(a+b)^(2)\left(a + b\right)^{2}$${(a+b)}^2$$

  ---

  • Roots
  $$\{\begin{array}{l}a=-b\\ b=-a\end{array}$$$$\left\{\begin{array}{l}a=-b\\ b=-a\end{array}\right.$${[a=-b],[b=-a]:}\left\{ \begin{array} {l} \,a = - b \\\, b = - a \end{array} \right.$$\{\begin{array}{l}a=-b\\ b=-a\end{array}$$

  ---

  • Result
  $$a^2+2ab+b^2$$$$a^2+2ab+b^2$$a^(2)+2ab+b^(2)a^{2} + 2 a b + b^{2}$$a^2+2ab+b^2$$

  ---

  • Expansion
  $$2ab+(a^2+b^2)$$$$2ab+\left(a^2+b^2\right)$$2ab+(a^(2)+b^(2))2 a b + \left(a^{2} + b^{2}\right)$$2ab+(a^2+b^2)$$

  ---

  • Graph
    

---

• Input
  $${\left(\frac{6}{5}\right)}^4\times {\left(\frac{6}{5}\right)}^2=$$$${\left(\frac{6}{5}\right)}^4\times {\left(\frac{6}{5}\right)}^2=$$((6)/(5))^(4)xx((6)/(5))^(2)=\left(\frac{6}{5}\right)^{4} \times\left(\frac{6}{5}\right)^{2}=$${\left(\frac{6}{5}\right)}^4\times {\left(\frac{6}{5}\right)}^2=$$

  ---

  • Result
  $$\frac{46656}{15625}$$$$\frac{46656}{15625}$$(46656)/(15625)\frac{46656}{15625}$$\frac{46656}{15625}$$

  ---

  • Numerical
  $$2.985984$$$$2.985984$$2.9859842.985984$$2.985984$$

---

• Input
  $$-\frac{1}{2}+\frac{\sqrt{33}}{2}$$$$-\frac{1}{2}+\frac{\sqrt{33}}{2}$$-(1)/(2)+(sqrt33)/(2)-\frac{1}{2}+\frac{\sqrt{33}}{2}$$-\frac{1}{2}+\frac{\sqrt{33}}{2}$$

  ---

  • Factorization
  $$\frac{-1+\sqrt{33}}{2}$$$$\frac{-1+\sqrt{33}}{2}$$(-1+sqrt33)/(2)\frac{-1 + \sqrt{33}}{2}$$\frac{-1+\sqrt{33}}{2}$$

  ---

  • Result
  $$-\frac{1}{2}+\frac{\sqrt{33}}{2}$$$$-\frac{1}{2}+\frac{\sqrt{33}}{2}$$-(1)/(2)+(sqrt33)/(2)- \frac{1}{2} + \frac{\sqrt{33}}{2}$$-\frac{1}{2}+\frac{\sqrt{33}}{2}$$

  ---

  • Numerical
  $$2.37228132326901$$$$2.37228132326901$$2.372281323269012.37228132326901$$2.37228132326901$$

---

• Input
  $$f(x)=\frac{2x}{3+x}$$$$f(x)=\frac{2x}{3+x}$$f(x)=(2x)/(3+x)f(x)=\frac{2 x}{3+x}$$f(x)=\frac{2x}{3+x}$$

  ---

  • Roots
  $$x=0$$$$x=0$$x=0x = 0$$x=0$$

  ---

  • Result
  $$\frac{2x}{x+3}$$$$\frac{2x}{x+3}$$(2x)/(x+3)\frac{2 x}{x + 3}$$\frac{2x}{x+3}$$

  ---

  • Graph
    

---

• Input
  $$-x^2+14x-20$$$$-x^2+14x-20$$-x^(2)+14 x-20-x^{2}+14 x-20$$-x^2+14x-20$$

  ---

  • Roots
  $$x\in \{7-\sqrt{29},\sqrt{29}+7\}$$$$x\in \left\{7-\sqrt{29},\sqrt{29}+7\right\}$$x in{7-sqrt29,sqrt29+7}x \in \left\{ 7 - \sqrt{29},\, \sqrt{29} + 7\right\}$$x\in \{7-\sqrt{29},\sqrt{29}+7\}$$

  ---

  • Result
  $$-x^2+14x-20$$$$-x^2+14x-20$$-x^(2)+14 x-20- x^{2} + 14 x - 20$$-x^2+14x-20$$

  ---

  • Expansion
  $$(-x^2+14x)-20$$$$\left(-x^2+14x\right)-20$$(-x^(2)+14 x)-20\left(- x^{2} + 14 x\right) - 20$$(-x^2+14x)-20$$

  ---

  • Graph
    

---

• Input
  $$\frac{\pi }{4}$$$$\frac{\pi }{4}$$(pi)/(4)\frac{\pi}{4}$$\frac{\pi }{4}$$

  ---

  • Numerical
  $$0.785398163397448$$$$0.785398163397448$$0.7853981633974480.785398163397448$$0.785398163397448$$

---

• Input
  $$\frac{2x^2-18}{x^4+2x^3-3x^2}\cdot \frac{x^2-11x+10}{x^2-13x+30}$$$$\frac{2x^2-18}{x^4+2x^3-3x^2}\cdot \frac{x^2-11x+10}{x^2-13x+30}$$(2x^(2)-18)/(x^(4)+2x^(3)-3x^(2))*(x^(2)-11 x+10)/(x^(2)-13 x+30)\frac{2 x^{2}-18}{x^{4}+2 x^{3}-3 x^{2}} \cdot \frac{x^{2}-11 x+10}{x^{2}-13 x+30}$$\frac{2x^2-18}{x^4+2x^3-3x^2}\cdot \frac{x^2-11x+10}{x^2-13x+30}$$

  ---

  • Result
  $$\frac{(2x^2-18)(x^2-11x+10)}{(x^2-13x+30)(x^4+2x^3-3x^2)}$$$$\frac{\left(2x^2-18\right)\left(x^2-11x+10\right)}{\left(x^2-13x+30\right)\left(x^4+2x^3-3x^2\right)}$$((2x^(2)-18)(x^(2)-11 x+10))/((x^(2)-13 x+30)(x^(4)+2x^(3)-3x^(2)))\frac{\left(2 x^{2} - 18\right) \left(x^{2} - 11 x + 10\right)}{\left(x^{2} - 13 x + 30\right) \left(x^{4} + 2 x^{3} - 3 x^{2}\right)}$$\frac{(2x^2-18)(x^2-11x+10)}{(x^2-13x+30)(x^4+2x^3-3x^2)}$$

  ---

  • Simplification
  $$\frac{2}{x^2}$$$$\frac{2}{x^2}$$(2)/(x^(2))\frac{2}{x^{2}}$$\frac{2}{x^2}$$

  ---

  • Expansion
  $$\frac{2x^4}{x^6-11x^5+x^4+99x^3-90x^2}-\frac{22x^3}{x^6-11x^5+x^4+99x^3-90x^2}+\frac{2x^2}{x^6-11x^5+x^4+99x^3-90x^2}+\frac{198x}{x^6-11x^5+x^4+99x^3-90x^2}-\frac{180}{x^6-11x^5+x^4+99x^3-90x^2}$$$$\frac{2x^4}{x^6-11x^5+x^4+99x^3-90x^2}-\frac{22x^3}{x^6-11x^5+x^4+99x^3-90x^2}+\frac{2x^2}{x^6-11x^5+x^4+99x^3-90x^2}+\frac{198x}{x^6-11x^5+x^4+99x^3-90x^2}-\frac{180}{x^6-11x^5+x^4+99x^3-90x^2}$$(2x^(4))/(x^(6)-11x^(5)+x^(4)+99x^(3)-90x^(2))-(22x^(3))/(x^(6)-11x^(5)+x^(4)+99x^(3)-90x^(2))+(2x^(2))/(x^(6)-11x^(5)+x^(4)+99x^(3)-90x^(2))+(198 x)/(x^(6)-11x^(5)+x^(4)+99x^(3)-90x^(2))-(180)/(x^(6)-11x^(5)+x^(4)+99x^(3)-90x^(2))\frac{2 x^{4}}{x^{6} - 11 x^{5} + x^{4} + 99 x^{3} - 90 x^{2}} - \frac{22 x^{3}}{x^{6} - 11 x^{5} + x^{4} + 99 x^{3} - 90 x^{2}} + \frac{2 x^{2}}{x^{6} - 11 x^{5} + x^{4} + 99 x^{3} - 90 x^{2}} + \frac{198 x}{x^{6} - 11 x^{5} + x^{4} + 99 x^{3} - 90 x^{2}} - \frac{180}{x^{6} - 11 x^{5} + x^{4} + 99 x^{3} - 90 x^{2}}$$\frac{2x^4}{x^6-11x^5+x^4+99x^3-90x^2}-\frac{22x^3}{x^6-11x^5+x^4+99x^3-90x^2}+\frac{2x^2}{x^6-11x^5+x^4+99x^3-90x^2}+\frac{198x}{x^6-11x^5+x^4+99x^3-90x^2}-\frac{180}{x^6-11x^5+x^4+99x^3-90x^2}$$

  ---

  • Graph
    

---

• Input
  $$x^2+y^3$$$$x^2+y^3$$x^(2)+y^(3)x^2 + y^3$$x^2+y^3$$

  ---

  • Roots
  $$\{\begin{array}{l}x=-\sqrt{-y^3},x=\sqrt{-y^3}\\ y=\sqrt[3]{-x^2},y=-\frac{\sqrt[3]{-x^2}}{2}-\frac{\sqrt{3}i\sqrt[3]{-x^2}}{2},y=-\frac{\sqrt[3]{-x^2}}{2}+\frac{\sqrt{3}i\sqrt[3]{-x^2}}{2}\end{array}$$$$\left\{\begin{array}{l}x=-\sqrt{-y^3},x=\sqrt{-y^3}\\ y=\sqrt[3]{-x^2},y=-\frac{\sqrt[3]{-x^2}}{2}-\frac{\sqrt{3}i\sqrt[3]{-x^2}}{2},y=-\frac{\sqrt[3]{-x^2}}{2}+\frac{\sqrt{3}i\sqrt[3]{-x^2}}{2}\end{array}\right.$${[x=-sqrt(-y^(3))","quad x=sqrt(-y^(3))],[y=root(3)(-x^(2))","quad y=-(root(3)(-x^(2)))/(2)-(sqrt3iroot(3)(-x^(2)))/(2)","quad y=-(root(3)(-x^(2)))/(2)+(sqrt3iroot(3)(-x^(2)))/(2)]:}\left\{ \begin{array} {l} \,x = - \sqrt{- y^{3}}\,,\quad x = \sqrt{- y^{3}} \\\, y = \sqrt[3]{- x^{2}}\,,\quad y = - \frac{\sqrt[3]{- x^{2}}}{2} - \frac{\sqrt{3} i \sqrt[3]{- x^{2}}}{2}\,,\quad y = - \frac{\sqrt[3]{- x^{2}}}{2} + \frac{\sqrt{3} i \sqrt[3]{- x^{2}}}{2} \end{array} \right.$$\{\begin{array}{l}x=-\sqrt{-y^3},x=\sqrt{-y^3}\\ y=\sqrt[3]{-x^2},y=-\frac{\sqrt[3]{-x^2}}{2}-\frac{\sqrt{3}i\sqrt[3]{-x^2}}{2},y=-\frac{\sqrt[3]{-x^2}}{2}+\frac{\sqrt{3}i\sqrt[3]{-x^2}}{2}\end{array}$$

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  • Result
  $$x^2+y^3$$$$x^2+y^3$$x^(2)+y^(3)x^{2} + y^{3}$$x^2+y^3$$

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  • Graph
    

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• Input
  $$x^2+y^2$$$$x^2+y^2$$x^(2)+y^(2)x^2 + y^2$$x^2+y^2$$

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  • Roots
  $$\{\begin{array}{l}x=-iy,x=iy\\ y=-ix,y=ix\end{array}$$$$\left\{\begin{array}{l}x=-iy,x=iy\\ y=-ix,y=ix\end{array}\right.$${[x=-iy","quad x=iy],[y=-ix","quad y=ix]:}\left\{ \begin{array} {l} \,x = - i y\,,\quad x = i y \\\, y = - i x\,,\quad y = i x \end{array} \right.$$\{\begin{array}{l}x=-iy,x=iy\\ y=-ix,y=ix\end{array}$$

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  • Result
  $$x^2+y^2$$$$x^2+y^2$$x^(2)+y^(2)x^{2} + y^{2}$$x^2+y^2$$

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  • Graph
    

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• Input
  $$8/(2+360)$$$$8/(2+360)$$8//(2+360)8 / (2 + 360)$$8/(2+360)$$

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  • Result
  $$\frac{4}{181}$$$$\frac{4}{181}$$(4)/(181)\frac{4}{181}$$\frac{4}{181}$$

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  • Numerical
  $$0.0220994475138122$$$$0.0220994475138122$$0.02209944751381220.0220994475138122$$0.0220994475138122$$

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  • Expansion
  $$\frac{8}{2+360}$$$$\frac{8}{2+360}$$(8)/(2+360)\frac{8}{2 + 360}$$\frac{8}{2+360}$$

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• Input
  $$\frac{0.3\cdot {10}^{-2}+0.8c}{1+\frac{0.3\cdot {10}^{-2}\cdot 0.8c}{c^2}}$$$$\frac{0.3\cdot {10}^{-2}+0.8c}{1+\frac{0.3\cdot {10}^{-2}\cdot 0.8c}{c^2}}$$(0.3*10^(-2)+0.8 c)/(1+(0.3*10^(-2)*0.8 c)/(c^(2)))\frac{0.3\cdot10^{-2} + 0.8c}{1 + \frac{0.3\cdot10^{-2}\cdot 0.8c}{c^2}}$$\frac{0.3\cdot {10}^{-2}+0.8c}{1+\frac{0.3\cdot {10}^{-2}\cdot 0.8c}{c^2}}$$

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  • Factorization
  $$\frac{0.8c(1.0c+0.00375)}{1.0c+0.0024}$$$$\frac{0.8c\left(1.0c+0.00375\right)}{1.0c+0.0024}$$(0.8 c(1.0 c+0.00375))/(1.0 c+0.0024)\frac{0.8 c \left(1.0 c + 0.00375\right)}{1.0 c + 0.0024}$$\frac{0.8c(1.0c+0.00375)}{1.0c+0.0024}$$

  ---

  • Roots
  $$c=-0.00375$$$$c=-0.00375$$c=-0.00375c = -0.00375$$c=-0.00375$$

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  • Result
  $$\frac{0.8c+0.003}{1+\frac{0.0024}{c}}$$$$\frac{0.8c+0.003}{1+\frac{0.0024}{c}}$$(0.8 c+0.003)/(1+(0.0024 )/(c))\frac{0.8 c + 0.003}{1 + \frac{0.0024}{c}}$$\frac{0.8c+0.003}{1+\frac{0.0024}{c}}$$

  ---

  • Simplification
  $$\frac{c(0.8c+0.003)}{c+0.0024}$$$$\frac{c\left(0.8c+0.003\right)}{c+0.0024}$$(c(0.8 c+0.003))/(c+0.0024)\frac{c \left(0.8 c + 0.003\right)}{c + 0.0024}$$\frac{c(0.8c+0.003)}{c+0.0024}$$

  ---

  • Expansion
  $$\frac{0.8c}{1+\frac{0.0024}{c}}+\frac{0.003}{1+\frac{0.0024}{c}}$$$$\frac{0.8c}{1+\frac{0.0024}{c}}+\frac{0.003}{1+\frac{0.0024}{c}}$$(0.8 c)/(1+(0.0024 )/(c))+(0.003)/(1+(0.0024 )/(c))\frac{0.8 c}{1 + \frac{0.0024}{c}} + \frac{0.003}{1 + \frac{0.0024}{c}}$$\frac{0.8c}{1+\frac{0.0024}{c}}+\frac{0.003}{1+\frac{0.0024}{c}}$$

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  • Graph
    

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• Input
  $$\frac{0.8c+0.3}{\frac{0.24}{c}+1}$$$$\frac{0.8c+0.3}{\frac{0.24}{c}+1}$$(0.8 c+0.3)/((0.24 )/(c)+1)\frac{0.8 c+0.3}{\frac{0.24}{c}+1}$$\frac{0.8c+0.3}{\frac{0.24}{c}+1}$$

  ---

  • Factorization
  $$\frac{0.8c(1.0c+0.375)}{1.0c+0.24}$$$$\frac{0.8c\left(1.0c+0.375\right)}{1.0c+0.24}$$(0.8 c(1.0 c+0.375))/(1.0 c+0.24)\frac{0.8 c \left(1.0 c + 0.375\right)}{1.0 c + 0.24}$$\frac{0.8c(1.0c+0.375)}{1.0c+0.24}$$

  ---

  • Roots
  $$c=-0.375$$$$c=-0.375$$c=-0.375c = -0.375$$c=-0.375$$

  ---

  • Result
  $$\frac{0.8c+0.3}{1+\frac{0.24}{c}}$$$$\frac{0.8c+0.3}{1+\frac{0.24}{c}}$$(0.8 c+0.3)/(1+(0.24 )/(c))\frac{0.8 c + 0.3}{1 + \frac{0.24}{c}}$$\frac{0.8c+0.3}{1+\frac{0.24}{c}}$$

  ---

  • Simplification
  $$\frac{c(0.8c+0.3)}{c+0.24}$$$$\frac{c\left(0.8c+0.3\right)}{c+0.24}$$(c(0.8 c+0.3))/(c+0.24)\frac{c \left(0.8 c + 0.3\right)}{c + 0.24}$$\frac{c(0.8c+0.3)}{c+0.24}$$

  ---

  • Expansion
  $$\frac{0.8c}{1+\frac{0.24}{c}}+\frac{0.3}{1+\frac{0.24}{c}}$$$$\frac{0.8c}{1+\frac{0.24}{c}}+\frac{0.3}{1+\frac{0.24}{c}}$$(0.8 c)/(1+(0.24 )/(c))+(0.3)/(1+(0.24 )/(c))\frac{0.8 c}{1 + \frac{0.24}{c}} + \frac{0.3}{1 + \frac{0.24}{c}}$$\frac{0.8c}{1+\frac{0.24}{c}}+\frac{0.3}{1+\frac{0.24}{c}}$$

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  • Graph
    

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• Input
  $$a^2+b^3$$$$a^2+b^3$$a^(2)+b^(3)a^2 + b^3$$a^2+b^3$$

  ---

  • Roots
  $$\{\begin{array}{l}a=-\sqrt{-b^3},a=\sqrt{-b^3}\\ b=\sqrt[3]{-a^2},b=-\frac{\sqrt[3]{-a^2}}{2}-\frac{\sqrt{3}i\sqrt[3]{-a^2}}{2},b=-\frac{\sqrt[3]{-a^2}}{2}+\frac{\sqrt{3}i\sqrt[3]{-a^2}}{2}\end{array}$$$$\left\{\begin{array}{l}a=-\sqrt{-b^3},a=\sqrt{-b^3}\\ b=\sqrt[3]{-a^2},b=-\frac{\sqrt[3]{-a^2}}{2}-\frac{\sqrt{3}i\sqrt[3]{-a^2}}{2},b=-\frac{\sqrt[3]{-a^2}}{2}+\frac{\sqrt{3}i\sqrt[3]{-a^2}}{2}\end{array}\right.$${[a=-sqrt(-b^(3))","quad a=sqrt(-b^(3))],[b=root(3)(-a^(2))","quad b=-(root(3)(-a^(2)))/(2)-(sqrt3iroot(3)(-a^(2)))/(2)","quad b=-(root(3)(-a^(2)))/(2)+(sqrt3iroot(3)(-a^(2)))/(2)]:}\left\{ \begin{array} {l} \,a = - \sqrt{- b^{3}}\,,\quad a = \sqrt{- b^{3}} \\\, b = \sqrt[3]{- a^{2}}\,,\quad b = - \frac{\sqrt[3]{- a^{2}}}{2} - \frac{\sqrt{3} i \sqrt[3]{- a^{2}}}{2}\,,\quad b = - \frac{\sqrt[3]{- a^{2}}}{2} + \frac{\sqrt{3} i \sqrt[3]{- a^{2}}}{2} \end{array} \right.$$\{\begin{array}{l}a=-\sqrt{-b^3},a=\sqrt{-b^3}\\ b=\sqrt[3]{-a^2},b=-\frac{\sqrt[3]{-a^2}}{2}-\frac{\sqrt{3}i\sqrt[3]{-a^2}}{2},b=-\frac{\sqrt[3]{-a^2}}{2}+\frac{\sqrt{3}i\sqrt[3]{-a^2}}{2}\end{array}$$

  ---

  • Result
  $$a^2+b^3$$$$a^2+b^3$$a^(2)+b^(3)a^{2} + b^{3}$$a^2+b^3$$

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  • Graph
    

---

• Input
  $$\sin (x)\times \sin (y)$$$$\sin (x)\times \sin (y)$$sin(x)xx sin(y)\sin(x) \times \sin(y)$$\sin (x)\times \sin (y)$$

  ---

  • Roots
  $$\{\begin{array}{l}x=0,x=\pi \\ y=0,y=\pi \end{array}$$$$\left\{\begin{array}{l}x=0,x=\pi \\ y=0,y=\pi \end{array}\right.$${[x=0","quad x=pi],[y=0","quad y=pi]:}\left\{ \begin{array} {l} \,x = 0\,,\quad x = \pi \\\, y = 0\,,\quad y = \pi \end{array} \right.$$\{\begin{array}{l}x=0,x=\pi \\ y=0,y=\pi \end{array}$$

  ---

  • Result
  $$\sin \left(x\right)\sin \left(y\right)$$$$\sin \left(x\right)\sin \left(y\right)$$sin (x)sin (y)\sin{\left(x \right)} \sin{\left(y \right)}$$\sin \left(x\right)\sin \left(y\right)$$

  ---

  • Graph
    

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• Input
  $$\sin (x)\cdot \sin (y)$$$$\sin (x)\cdot \sin (y)$$sin(x)*sin(y)\sin (x) \cdot \sin (y)$$\sin (x)\cdot \sin (y)$$

  ---

  • Roots
  $$\{\begin{array}{l}x=0,x=\pi \\ y=0,y=\pi \end{array}$$$$\left\{\begin{array}{l}x=0,x=\pi \\ y=0,y=\pi \end{array}\right.$${[x=0","quad x=pi],[y=0","quad y=pi]:}\left\{ \begin{array} {l} \,x = 0\,,\quad x = \pi \\\, y = 0\,,\quad y = \pi \end{array} \right.$$\{\begin{array}{l}x=0,x=\pi \\ y=0,y=\pi \end{array}$$

  ---

  • Result
  $$\sin \left(x\right)\sin \left(y\right)$$$$\sin \left(x\right)\sin \left(y\right)$$sin (x)sin (y)\sin{\left(x \right)} \sin{\left(y \right)}$$\sin \left(x\right)\sin \left(y\right)$$

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  • Graph
    

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• Input
  $$x^2$$$$x^2$$x^(2)x^{2}$$x^2$$

  ---

  • Roots
  $$x=0$$$$x=0$$x=0x = 0$$x=0$$

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  • Graph
    

---

• Input
  $$x^{2/3}+y^{2/3}$$$$x^{2/3}+y^{2/3}$$x^(2//3)+y^(2//3)x^{2 / 3}+y^{2 / 3}$$x^{2/3}+y^{2/3}$$

  ---

  • Roots
  $$\{\begin{array}{l}x=-iy,x=iy\\ y=-ix,y=ix\end{array}$$$$\left\{\begin{array}{l}x=-iy,x=iy\\ y=-ix,y=ix\end{array}\right.$${[x=-iy","quad x=iy],[y=-ix","quad y=ix]:}\left\{ \begin{array} {l} \,x = - i y\,,\quad x = i y \\\, y = - i x\,,\quad y = i x \end{array} \right.$$\{\begin{array}{l}x=-iy,x=iy\\ y=-ix,y=ix\end{array}$$

  ---

  • Result
  $$x^{\frac{2}{3}}+y^{\frac{2}{3}}$$$$x^{\frac{2}{3}}+y^{\frac{2}{3}}$$x^((2)/(3))+y^((2)/(3))x^{\frac{2}{3}} + y^{\frac{2}{3}}$$x^{\frac{2}{3}}+y^{\frac{2}{3}}$$

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  • Graph
    

---

• Input
  $$f(x)=\{\begin{array}{ccc}x{e}^{2x}& \text{si}& x<0\\ \frac{\ln (x+1)}{x+1}& \text{si}& x\ge 0\end{array}$$$$f(x)=\left\{\begin{array}{ccc}x{e}^{2x}& \text{ si }& x<0\\ \frac{\ln (x+1)}{x+1}& \text{ si }& x\ge 0\end{array}\right.$$f(x)={[xe^(2x)," si ",x < 0],[(ln(x+1))/(x+1)," si ",x >= 0]:}f(x)=\left\{\begin{array}{ccc} x e^{2 x} & \text { si } & x<0 \\ \frac{\ln (x+1)}{x+1} & \text { si } & x \geq 0 \end{array}\right.$$f(x)=\{\begin{array}{ccc}x{e}^{2x}& \text{ si }& x<0\\ \frac{\ln (x+1)}{x+1}& \text{ si }& x\ge 0\end{array}$$

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  • Roots
  $$x=0$$$$x=0$$x=0x = 0$$x=0$$

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  • Graph
    

---

Concrete

---

• Input
  $$\sum _{n=1}^{7}2(-2{)}^{n-1}$$$$\sum _{n=1}^7 2(-2{)}^{n-1}$$sum_(n=1)^(7)2(-2)^(n-1)\sum_{n=1}^{7} 2(-2)^{n-1}$$\sum _{n=1}^{7}2(-2{)}^{n-1}$$

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  • Result
  $$86$$$$86$$8686$$86$$

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  • Simplification
  $$-\sum _{n=1}^7{(-1)}^n{2}^n$$$$-\sum _{n=1}^7 {\left(-1\right)}^n{2}^n$$-sum_(n=1)^(7)(-1)^(n)2^(n)- \sum_{n=1}^{7} \left(-1\right)^{n} 2^{n}$$-\sum _{n=1}^7{(-1)}^n{2}^n$$

---

Relationals

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• Input
  $$(u+5)(u+3)\le -1$$$$(u+5)(u+3)\le -1$$(u+5)(u+3) <= -1(u+5)(u+3) \leq-1$$(u+5)(u+3)\le -1$$

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  • Solution
  $$u=-4$$$$u=-4$$u=-4u = -4$$u=-4$$

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  • Simplification
  $$u^2+8u\le -16$$$$u^2+8u\le -16$$u^(2)+8u <= -16u^{2} + 8 u \leq -16$$u^2+8u\le -16$$

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  • Graph
    

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• Input
  $$x-y\le 10$$$$x-y\le 10$$x-y <= 10x - y \leq 10$$x-y\le 10$$

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  • Solution
  $$\{\begin{array}{l}x\le y+10\wedge -\mathrm{\infty }<x\\ y\ge x-10\wedge y<\mathrm{\infty }\end{array}$$$$\left\{\begin{array}{l}x\le y+10\wedge -\mathrm{\infty }<x\\ y\ge x-10\wedge y<\mathrm{\infty }\end{array}\right.$${[x <= y+10^^-oo < x],[y >= x-10^^y < oo]:}\left\{ \begin{array} {l} \,x \leq y + 10 \wedge -\infty < x \\\, y \geq x - 10 \wedge y < \infty \end{array} \right.$$\{\begin{array}{l}x\le y+10\wedge -\mathrm{\infty }<x\\ y\ge x-10\wedge y<\mathrm{\infty }\end{array}$$

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  • Graph
    

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• Input
  $$x^2+y^3\ge 4$$$$x^2+y^3\ge 4$$x^(2)+y^(3) >= 4x^{2}+y^{3} \geq 4$$x^2+y^3\ge 4$$

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  • Graph
    

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• Input
  $$x^4+y^6\le 3$$$$x^4+y^6\le 3$$x^(4)+y^(6) <= 3x^4 + y^6 \leq 3$$x^4+y^6\le 3$$

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  • Graph
    

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• Input
  $$x^2+y^3\le 3$$$$x^2+y^3\le 3$$x^(2)+y^(3) <= 3x^2 + y^3 \leq 3$$x^2+y^3\le 3$$

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  • Graph
    

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• Input
  $$x+y\le 10$$$$x+y\le 10$$x+y <= 10x + y \leq 10$$x+y\le 10$$

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  • Solution
  $$\{\begin{array}{l}x\le 10-y\wedge -\mathrm{\infty }<x\\ y\le 10-x\wedge -\mathrm{\infty }<y\end{array}$$$$\left\{\begin{array}{l}x\le 10-y\wedge -\mathrm{\infty }<x\\ y\le 10-x\wedge -\mathrm{\infty }<y\end{array}\right.$${[x <= 10-y^^-oo < x],[y <= 10-x^^-oo < y]:}\left\{ \begin{array} {l} \,x \leq 10 - y \wedge -\infty < x \\\, y \leq 10 - x \wedge -\infty < y \end{array} \right.$$\{\begin{array}{l}x\le 10-y\wedge -\mathrm{\infty }<x\\ y\le 10-x\wedge -\mathrm{\infty }<y\end{array}$$

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  • Graph
    

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• Input
  $$x^2+y^2\le 20$$$$x^2+y^2\le 20$$x^(2)+y^(2) <= 20x^2 + y^2 \leq 20$$x^2+y^2\le 20$$

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  • Graph
    

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• Input
  $$x^2+y^2\le 10$$$$x^2+y^2\le 10$$x^(2)+y^(2) <= 10x^{2}+y^{2} \leq 10$$x^2+y^2\le 10$$

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  • Graph
    

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• Input
  $$x^2-y^2\le 10$$$$x^2-y^2\le 10$$x^(2)-y^(2) <= 10x^{2}-y^{2} \leq 10$$x^2-y^2\le 10$$

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  • Graph
    

---

Equation

---

• Input
  $$x^{\frac{2}{3}}-4x^{\frac{1}{3}}-5=0$$$$x^{\frac{2}{3}}-4x^{\frac{1}{3}}-5=0$$x^((2)/(3))-4x^((1)/(3))-5=0x^{\frac{2}{3}}-4 x^{\frac{1}{3}}-5=0$$x^{\frac{2}{3}}-4x^{\frac{1}{3}}-5=0$$

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  • Solution
  $$x=125$$$$x=125$$x=125x = 125$$x=125$$

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  • Simplification
  $$-x^{\frac{2}{3}}+4\sqrt[3]{x}+5=0$$$$-x^{\frac{2}{3}}+4\sqrt[3]{x}+5=0$$-x^((2)/(3))+4root(3)(x)+5=0- x^{\frac{2}{3}} + 4 \sqrt[3]{x} + 5 = 0$$-x^{\frac{2}{3}}+4\sqrt[3]{x}+5=0$$

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  • Graph
    

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• Input
  $$\left|\begin{array}{ccc}x& 2& 6\\ 6& x& 0\\ 5& 1& -6\end{array}\right|=108$$$$\left|\begin{array}{ccc}x& 2& 6\\ 6& x& 0\\ 5& 1& -6\end{array}\right|=108$$|[x,2,6],[6,x,0],[5,1,-6]|=108\left|\begin{array}{ccc}x & 2 & 6 \\ 6 & x & 0 \\ 5 & 1 & -6\end{array}\right|=108$$\left|\begin{array}{ccc}x& 2& 6\\ 6& x& 0\\ 5& 1& -6\end{array}\right|=108$$

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  • Solution
  $$x\in \{-5,0\}$$$$x\in \left\{-5,0\right\}$$x in{-5,0}x \in \left\{ -5,\, 0\right\}$$x\in \{-5,0\}$$

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  • Simplification
  $$x^2+5x=0$$$$x^2+5x=0$$x^(2)+5x=0x^{2} + 5 x = 0$$x^2+5x=0$$

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  • Graph
    

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• Input
  $$x^2+2x+1=0$$$$x^2+2x+1=0$$x^(2)+2x+1=0x ^ 2 + 2 x + 1 = 0$$x^2+2x+1=0$$

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  • Solution
  $$x=-1$$$$x=-1$$x=-1x = -1$$x=-1$$

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  • Simplification
  $$x^2+2x=-1$$$$x^2+2x=-1$$x^(2)+2x=-1x^{2} + 2 x = -1$$x^2+2x=-1$$

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  • Graph
    

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• Input
  $$\cot ({180}^{\circ }-\theta )=\cot \theta$$$$\cot \left({180}^{\circ }-\theta \right)=\cot \theta$$cot(180^(@)-theta)=cot theta\cot \left(180^{\circ}-\theta\right)=\cot \theta$$\cot ({180}^{\circ }-\theta )=\cot \theta$$

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  • Solution
  $$\theta =\frac{\pi }{2}$$$$\theta =\frac{\pi }{2}$$theta=(pi)/(2)\theta = \frac{\pi}{2}$$\theta =\frac{\pi }{2}$$

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  • Simplification
  $$\cot \left(\theta \right)=-\cot \left(\theta \right)$$$$\cot \left(\theta \right)=-\cot \left(\theta \right)$$cot (theta)=-cot (theta)\cot{\left(\theta \right)} = - \cot{\left(\theta \right)}$$\cot \left(\theta \right)=-\cot \left(\theta \right)$$

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  • Graph
    

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• Input
  $$9^x\cdot 3^{x^2}={81}^2$$$$9^x\cdot 3^{x^2}={81}^2$$9^(x)*3^(x^(2))=81^(2)9^{x} \cdot 3^{x^{2}}=81^{2}$$9^x\cdot 3^{x^2}={81}^2$$

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  • Solution
  $$x\in \{-4,2\}$$$$x\in \left\{-4,2\right\}$$x in{-4,2}x \in \left\{ -4,\, 2\right\}$$x\in \{-4,2\}$$

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  • Simplification
  $$3^{x(x+2)}=6561$$$$3^{x\left(x+2\right)}=6561$$3^(x(x+2))=65613^{x \left(x + 2\right)} = 6561$$3^{x(x+2)}=6561$$

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  • Graph
    

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• Input
  $$\sqrt{x+73}=x+1$$$$\sqrt{x+73}=x+1$$sqrt(x+73)=x+1\sqrt{x+73}=x+1$$\sqrt{x+73}=x+1$$

  ---

  • Solution
  $$x=8$$$$x=8$$x=8x = 8$$x=8$$

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  • Simplification
  $$x+1=\sqrt{x+73}$$$$x+1=\sqrt{x+73}$$x+1=sqrt(x+73)x + 1 = \sqrt{x + 73}$$x+1=\sqrt{x+73}$$

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  • Graph
    

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• Input
  $$(\genfrac{}{}{0ex}{}{5}{2})=2y$$$$(\genfrac{}{}{0ex}{}{5}{2})=2y$$((5)/(2))=2y\binom{5}{2} = 2 y$$(\genfrac{}{}{0ex}{}{5}{2})=2y$$

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  • Solution
  $$y=5$$$$y=5$$y=5y = 5$$y=5$$

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  • Graph
    

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• Input
  $${\int }_0^1{x}^{2}dx=2y$$$${\int }_0^1 x^{2}dx=2y$$int_(0)^(1)x^(2)dx=2y\int_0^1 x^2 dx = 2 y$${\int }_0^1{x}^{2}dx=2y$$

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  • Solution
  $$y=\frac{1}{6}$$$$y=\frac{1}{6}$$y=(1)/(6)y = \frac{1}{6}$$y=\frac{1}{6}$$

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  • Simplification
  $$y=\frac{\underset{0}{\overset{1}{\int }}{x}^{2}dx}{2}$$$$y=\frac{\underset{0}{\overset{1}{\int }} x^{2}dx}{2}$$y=(int_(0)^(1)x^(2)dx)/(2)y = \frac{\int\limits_{0}^{1} x^{2}\, dx}{2}$$y=\frac{\underset{0}{\overset{1}{\int }}{x}^{2}dx}{2}$$

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  • Graph
    

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• Input
  $$5^{7x+2}=2^{x-3}$$$$5^{7x+2}=2^{x-3}$$5^(7x+2)=2^(x-3)5^{7 x+2}=2^{x-3}$$5^{7x+2}=2^{x-3}$$

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  • Solution
  $$x=\ln \left({200}^{\frac{1}{\ln \left(\frac{2}{78125}\right)}}\right)$$$$x=\ln \left({200}^{\frac{1}{\ln \left(\frac{2}{78125}\right)}}\right)$$x=ln (200^((1)/(ln (((2)/(78125))))))x = \ln{\left(200^{\frac{1}{\ln{\left(\frac{2}{78125} \right)}}} \right)}$$x=\ln \left({200}^{\frac{1}{\ln \left(\frac{2}{78125}\right)}}\right)$$

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  • Simplification
  $$2^{x-3}=5^{7x+2}$$$$2^{x-3}=5^{7x+2}$$2^(x-3)=5^(7x+2)2^{x - 3} = 5^{7 x + 2}$$2^{x-3}=5^{7x+2}$$

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  • Graph
    

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• Input
  $$\sin (4\pi x)=\frac{\sqrt{3}}{2}$$$$\sin (4\pi x)=\frac{\sqrt{3}}{2}$$sin(4pi x)=(sqrt3)/(2)\sin (4 \pi x)=\frac{\sqrt{3}}{2}$$\sin (4\pi x)=\frac{\sqrt{3}}{2}$$

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  • Solution
  $$x\in \{\frac{1}{12},\frac{1}{6}\}$$$$x\in \left\{\frac{1}{12},\frac{1}{6}\right\}$$x in{(1)/(12),(1)/(6)}x \in \left\{ \frac{1}{12},\, \frac{1}{6}\right\}$$x\in \{\frac{1}{12},\frac{1}{6}\}$$

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  • Simplification
  $$\sin \left(4\pi x\right)=\frac{\sqrt{3}}{2}$$$$\sin \left(4\pi x\right)=\frac{\sqrt{3}}{2}$$sin (4pi x)=(sqrt3)/(2)\sin{\left(4 \pi x \right)} = \frac{\sqrt{3}}{2}$$\sin \left(4\pi x\right)=\frac{\sqrt{3}}{2}$$

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  • Graph
    

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• Input
  $${\log }_{x}64=3$$$${\log }_{x}64=3$$log_(x)64=3\log _{x} 64=3$${\log }_{x}64=3$$

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  • Solution
  $$x=4$$$$x=4$$x=4x = 4$$x=4$$

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  • Simplification
  $${\log }_x\left(64\right)=3$$$${\log }_x\left(64\right)=3$$log_(x)(64)=3\log_{x} {\left(64 \right)} = 3$${\log }_x\left(64\right)=3$$

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  • Graph
    

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• Input
  $$\frac{\sqrt{4-3x}}{\sqrt{3x}}=2$$$$\frac{\sqrt{4-3x}}{\sqrt{3x}}=2$$(sqrt(4-3x))/(sqrt(3x))=2\frac{\sqrt{4-3 x}}{\sqrt{3 x}}=2$$\frac{\sqrt{4-3x}}{\sqrt{3x}}=2$$

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  • Solution
  $$x=\frac{4}{15}$$$$x=\frac{4}{15}$$x=(4)/(15)x = \frac{4}{15}$$x=\frac{4}{15}$$

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  • Simplification
  $$\frac{\sqrt{12-9x}}{3\sqrt{x}}=2$$$$\frac{\sqrt{12-9x}}{3\sqrt{x}}=2$$(sqrt(12-9x))/(3sqrtx)=2\frac{\sqrt{12 - 9 x}}{3 \sqrt{x}} = 2$$\frac{\sqrt{12-9x}}{3\sqrt{x}}=2$$

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• Input
  $${\log }_{49}\sqrt[3]{7}=x$$$${\log }_{49}\sqrt[3]{7}=x$$log_(49)root(3)(7)=x\log _{49} \sqrt[3]{7}=x$${\log }_{49}\sqrt[3]{7}=x$$

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  • Solution
  $$x=\frac{1}{6}$$$$x=\frac{1}{6}$$x=(1)/(6)x = \frac{1}{6}$$x=\frac{1}{6}$$

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  • Graph
    

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• Input
  $$x^2=4$$$$x^2=4$$x^(2)=4x ^ 2 = 4$$x^2=4$$

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  • Solution
  $$x\in \{-2,2\}$$$$x\in \left\{-2,2\right\}$$x in{-2,2}x \in \left\{ -2,\, 2\right\}$$x\in \{-2,2\}$$

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  • Simplification
  $$x^2=4$$$$x^2=4$$x^(2)=4x^{2} = 4$$x^2=4$$

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  • Graph
    

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• Input
  $$\frac{3}{4}=3x$$$$\frac{3}{4}=3x$$(3)/(4)=3x\frac{3}{4} = 3 x$$\frac{3}{4}=3x$$

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  • Solution
  $$x=\frac{1}{4}$$$$x=\frac{1}{4}$$x=(1)/(4)x = \frac{1}{4}$$x=\frac{1}{4}$$

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  • Graph
    

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• Input
  $$\frac{3}{a+2}+\frac{4}{a-1}=0$$$$\frac{3}{a+2}+\frac{4}{a-1}=0$$(3)/(a+2)+(4)/(a-1)=0\frac{3}{a+2}+\frac{4}{a-1}=0$$\frac{3}{a+2}+\frac{4}{a-1}=0$$

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  • Solution
  $$a=-\frac{5}{7}$$$$a=-\frac{5}{7}$$a=-(5)/(7)a = - \frac{5}{7}$$a=-\frac{5}{7}$$

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  • Simplification
  $$\frac{7a+5}{(a-1)(a+2)}=0$$$$\frac{7a+5}{\left(a-1\right)\left(a+2\right)}=0$$(7a+5)/((a-1)(a+2))=0\frac{7 a + 5}{\left(a - 1\right) \left(a + 2\right)} = 0$$\frac{7a+5}{(a-1)(a+2)}=0$$

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• Input
  $$y=\frac{2x}{3+x}$$$$y=\frac{2x}{3+x}$$y=(2x)/(3+x)y=\frac{2 x}{3+x}$$y=\frac{2x}{3+x}$$

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  • Solution
  $$\{\begin{array}{l}x=-\frac{3y}{y-2}\\ y=\frac{2x}{x+3}\end{array}$$$$\left\{\begin{array}{l}x=-\frac{3y}{y-2}\\ y=\frac{2x}{x+3}\end{array}\right.$${[x=-(3y)/(y-2)],[y=(2x)/(x+3)]:}\left\{ \begin{array} {l} \,x = - \frac{3 y}{y - 2} \\\, y = \frac{2 x}{x + 3} \end{array} \right.$$\{\begin{array}{l}x=-\frac{3y}{y-2}\\ y=\frac{2x}{x+3}\end{array}$$

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  • Simplification
  $$y=\frac{2x}{x+3}$$$$y=\frac{2x}{x+3}$$y=(2x)/(x+3)y = \frac{2 x}{x + 3}$$y=\frac{2x}{x+3}$$

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  • Graph
    

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• Input
  $$x+y=10$$$$x+y=10$$x+y=10x + y = 10$$x+y=10$$

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  • Solution
  $$\{\begin{array}{l}x=10-y\\ y=10-x\end{array}$$$$\left\{\begin{array}{l}x=10-y\\ y=10-x\end{array}\right.$${[x=10-y],[y=10-x]:}\left\{ \begin{array} {l} \,x = 10 - y \\\, y = 10 - x \end{array} \right.$$\{\begin{array}{l}x=10-y\\ y=10-x\end{array}$$

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  • Graph
    

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• Input
  $$y^2+x^2=z^2$$$$y^2+x^2=z^2$$y^(2)+x^(2)=z^(2)y^{2}+x^{2}=z^{2}$$y^2+x^2=z^2$$

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  • Solution
  $$\{\begin{array}{l}x=-\sqrt{-y^2+z^2},x=\sqrt{-y^2+z^2}\\ y=-\sqrt{-x^2+z^2},y=\sqrt{-x^2+z^2}\\ z=-\sqrt{x^2+y^2},z=\sqrt{x^2+y^2}\end{array}$$$$\left\{\begin{array}{l}x=-\sqrt{-y^2+z^2},x=\sqrt{-y^2+z^2}\\ y=-\sqrt{-x^2+z^2},y=\sqrt{-x^2+z^2}\\ z=-\sqrt{x^2+y^2},z=\sqrt{x^2+y^2}\end{array}\right.$${[x=-sqrt(-y^(2)+z^(2))","quad x=sqrt(-y^(2)+z^(2))],[y=-sqrt(-x^(2)+z^(2))","quad y=sqrt(-x^(2)+z^(2))],[z=-sqrt(x^(2)+y^(2))","quad z=sqrt(x^(2)+y^(2))]:}\left\{ \begin{array} {l} \,x = - \sqrt{- y^{2} + z^{2}}\,,\quad x = \sqrt{- y^{2} + z^{2}} \\\, y = - \sqrt{- x^{2} + z^{2}}\,,\quad y = \sqrt{- x^{2} + z^{2}} \\\, z = - \sqrt{x^{2} + y^{2}}\,,\quad z = \sqrt{x^{2} + y^{2}} \end{array} \right.$$\{\begin{array}{l}x=-\sqrt{-y^2+z^2},x=\sqrt{-y^2+z^2}\\ y=-\sqrt{-x^2+z^2},y=\sqrt{-x^2+z^2}\\ z=-\sqrt{x^2+y^2},z=\sqrt{x^2+y^2}\end{array}$$

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  • Simplification
  $$z^2=x^2+y^2$$$$z^2=x^2+y^2$$z^(2)=x^(2)+y^(2)z^{2} = x^{2} + y^{2}$$z^2=x^2+y^2$$

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• Input
  $$x^2+y^2=100$$$$x^2+y^2=100$$x^(2)+y^(2)=100x^2 + y^2 = 100$$x^2+y^2=100$$

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  • Solution
  $$\{\begin{array}{l}x=-\sqrt{100-y^2},x=\sqrt{100-y^2}\\ y=-\sqrt{100-x^2},y=\sqrt{100-x^2}\end{array}$$$$\left\{\begin{array}{l}x=-\sqrt{100-y^2},x=\sqrt{100-y^2}\\ y=-\sqrt{100-x^2},y=\sqrt{100-x^2}\end{array}\right.$${[x=-sqrt(100-y^(2))","quad x=sqrt(100-y^(2))],[y=-sqrt(100-x^(2))","quad y=sqrt(100-x^(2))]:}\left\{ \begin{array} {l} \,x = - \sqrt{100 - y^{2}}\,,\quad x = \sqrt{100 - y^{2}} \\\, y = - \sqrt{100 - x^{2}}\,,\quad y = \sqrt{100 - x^{2}} \end{array} \right.$$\{\begin{array}{l}x=-\sqrt{100-y^2},x=\sqrt{100-y^2}\\ y=-\sqrt{100-x^2},y=\sqrt{100-x^2}\end{array}$$

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  • Simplification
  $$x^2+y^2=100$$$$x^2+y^2=100$$x^(2)+y^(2)=100x^{2} + y^{2} = 100$$x^2+y^2=100$$

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  • Graph
    

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• Input
  $$x^2+y^3=100$$$$x^2+y^3=100$$x^(2)+y^(3)=100x^2 + y^3 = 100$$x^2+y^3=100$$

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  • Solution
  $$\{\begin{array}{l}x=-\sqrt{100-y^3},x=\sqrt{100-y^3}\\ y=\sqrt[3]{100-x^2},y=-\frac{\sqrt[3]{100-x^2}}{2}-\frac{\sqrt{3}i\sqrt[3]{100-x^2}}{2},y=-\frac{\sqrt[3]{100-x^2}}{2}+\frac{\sqrt{3}i\sqrt[3]{100-x^2}}{2}\end{array}$$$$\left\{\begin{array}{l}x=-\sqrt{100-y^3},x=\sqrt{100-y^3}\\ y=\sqrt[3]{100-x^2},y=-\frac{\sqrt[3]{100-x^2}}{2}-\frac{\sqrt{3}i\sqrt[3]{100-x^2}}{2},y=-\frac{\sqrt[3]{100-x^2}}{2}+\frac{\sqrt{3}i\sqrt[3]{100-x^2}}{2}\end{array}\right.$${[x=-sqrt(100-y^(3))","quad x=sqrt(100-y^(3))],[y=root(3)(100-x^(2))","quad y=-(root(3)(100-x^(2)))/(2)-(sqrt3iroot(3)(100-x^(2)))/(2)","quad y=-(root(3)(100-x^(2)))/(2)+(sqrt3iroot(3)(100-x^(2)))/(2)]:}\left\{ \begin{array} {l} \,x = - \sqrt{100 - y^{3}}\,,\quad x = \sqrt{100 - y^{3}} \\\, y = \sqrt[3]{100 - x^{2}}\,,\quad y = - \frac{\sqrt[3]{100 - x^{2}}}{2} - \frac{\sqrt{3} i \sqrt[3]{100 - x^{2}}}{2}\,,\quad y = - \frac{\sqrt[3]{100 - x^{2}}}{2} + \frac{\sqrt{3} i \sqrt[3]{100 - x^{2}}}{2} \end{array} \right.$$\{\begin{array}{l}x=-\sqrt{100-y^3},x=\sqrt{100-y^3}\\ y=\sqrt[3]{100-x^2},y=-\frac{\sqrt[3]{100-x^2}}{2}-\frac{\sqrt{3}i\sqrt[3]{100-x^2}}{2},y=-\frac{\sqrt[3]{100-x^2}}{2}+\frac{\sqrt{3}i\sqrt[3]{100-x^2}}{2}\end{array}$$

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  • Simplification
  $$x^2+y^3=100$$$$x^2+y^3=100$$x^(2)+y^(3)=100x^{2} + y^{3} = 100$$x^2+y^3=100$$

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  • Graph
    

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• Input
  $$u=\frac{0.3\cdot {10}^{-2}+2.4\cdot {10}^8}{1+(0.3\cdot {10}^{-2})\cdot (2.66851\cdot {10}^{-9})}$$$$u=\frac{0.3\cdot {10}^{-2}+2.4\cdot {10}^8}{1+(0.3\cdot {10}^{-2})\cdot (2.66851\cdot {10}^{-9})}$$u=(0.3*10^(-2)+2.4*10^(8))/(1+(0.3*10^(-2))*(2.66851*10^(-9)))u=\frac{0.3 \cdot 10^{-2} + 2.4\cdot10^8}{1+ (0.3 \cdot 10^{-2}) \cdot (2.66851\cdot10^{-9})}$$u=\frac{0.3\cdot {10}^{-2}+2.4\cdot {10}^8}{1+(0.3\cdot {10}^{-2})\cdot (2.66851\cdot {10}^{-9})}$$

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  • Solution
  $$u=240000000.001079$$$$u=240000000.001079$$u=240000000.001079u = 240000000.001079$$u=240000000.001079$$

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  • Graph
    

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• Input
  $$u=\frac{u^{\prime }+v}{1+u^{\prime }v/c^2}$$$$u=\frac{u^{\prime }+v}{1+u^{\prime }v/c^2}$$u=(u^(')+v)/(1+u^(')v//c^(2))u=\frac{u^{\prime}+v}{1+u^{\prime} v / c^{2}}$$u=\frac{u^{\prime }+v}{1+u^{\prime }v/c^2}$$

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  • Solution
  $$\{\begin{array}{l}c=-\sqrt{\frac{u{u}^{\prime }v}{-u+u^{\prime }+v}},c=\sqrt{\frac{u{u}^{\prime }v}{-u+u^{\prime }+v}}\\ u=\frac{c^2(u^{\prime }+v)}{c^2+u^{\prime }v}\\ u^{\prime }=\frac{c^2(u-v)}{c^2-uv}\\ v=\frac{c^2(u-u^{\prime })}{c^2-u{u}^{\prime }}\end{array}$$$$\left\{\begin{array}{l}c=-\sqrt{\frac{u{u}^{\prime }v}{-u+u^{\prime }+v}},c=\sqrt{\frac{u{u}^{\prime }v}{-u+u^{\prime }+v}}\\ u=\frac{c^2\left(u^{\prime }+v\right)}{c^2+u^{\prime }v}\\ u^{\prime }=\frac{c^2\left(u-v\right)}{c^2-uv}\\ v=\frac{c^2\left(u-u^{\prime }\right)}{c^2-u{u}^{\prime }}\end{array}\right.$${[c=-sqrt((uu^(')v)/(-u+u^(')+v))","quad c=sqrt((uu^(')v)/(-u+u^(')+v))],[u=(c^(2)(u^(')+v))/(c^(2)+u^(')v)],[u^(')=(c^(2)(u-v))/(c^(2)-uv)],[v=(c^(2)(u-u^(')))/(c^(2)-uu^('))]:}\left\{ \begin{array} {l} \,c = - \sqrt{\frac{u u^{\prime} v}{- u + u^{\prime} + v}}\,,\quad c = \sqrt{\frac{u u^{\prime} v}{- u + u^{\prime} + v}} \\\, u = \frac{c^{2} \left(u^{\prime} + v\right)}{c^{2} + u^{\prime} v} \\\, u^{\prime} = \frac{c^{2} \left(u - v\right)}{c^{2} - u v} \\\, v = \frac{c^{2} \left(u - u^{\prime}\right)}{c^{2} - u u^{\prime}} \end{array} \right.$$\{\begin{array}{l}c=-\sqrt{\frac{u{u}^{\prime }v}{-u+u^{\prime }+v}},c=\sqrt{\frac{u{u}^{\prime }v}{-u+u^{\prime }+v}}\\ u=\frac{c^2(u^{\prime }+v)}{c^2+u^{\prime }v}\\ u^{\prime }=\frac{c^2(u-v)}{c^2-uv}\\ v=\frac{c^2(u-u^{\prime })}{c^2-u{u}^{\prime }}\end{array}$$

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  • Simplification
  $$u=\frac{c^2(u^{\prime }+v)}{c^2+u^{\prime }v}$$$$u=\frac{c^2\left(u^{\prime }+v\right)}{c^2+u^{\prime }v}$$u=(c^(2)(u^(')+v))/(c^(2)+u^(')v)u = \frac{c^{2} \left(u^{\prime} + v\right)}{c^{2} + u^{\prime} v}$$u=\frac{c^2(u^{\prime }+v)}{c^2+u^{\prime }v}$$

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• Input
  $${\int }_a^b{f}^{\prime }(x)dx=f(b)-f(a)$$$${\int }_a^b f^{\prime }(x)dx=f(b)-f(a)$$int_(a)^(b)f^(')(x)dx=f(b)-f(a)\int_{a}^{b} f^{\prime}(x) d x=f(b)-f(a)$${\int }_a^b{f}^{\prime }(x)dx=f(b)-f(a)$$

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  • Simplification
  $$\text{True}$$$$\text{True}$$"True"\text{True}$$\text{True}$$

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• Input
  $$y^2=x^{2}y+x^5$$$$y^2=x^{2}y+x^5$$y^(2)=x^(2)y+x^(5)y^{2}=x^{2} y+x^{5}$$y^2=x^{2}y+x^5$$

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  • Simplification
  $$y^2=x^2(x^3+y)$$$$y^2=x^2\left(x^3+y\right)$$y^(2)=x^(2)(x^(3)+y)y^{2} = x^{2} \left(x^{3} + y\right)$$y^2=x^2(x^3+y)$$

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  • Graph
    

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• Input
  $$x^3=10$$$$x^3=10$$x^(3)=10x^{3}=10$$x^3=10$$

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  • Solution
  $$x\in \{\sqrt[3]{10},-\frac{\sqrt[3]{10}}{2}-\frac{\sqrt[3]{10}\sqrt{3}i}{2},-\frac{\sqrt[3]{10}}{2}+\frac{\sqrt[3]{10}\sqrt{3}i}{2}\}$$$$x\in \left\{\sqrt[3]{10},-\frac{\sqrt[3]{10}}{2}-\frac{\sqrt[3]{10}\sqrt{3}i}{2},-\frac{\sqrt[3]{10}}{2}+\frac{\sqrt[3]{10}\sqrt{3}i}{2}\right\}$$x in{root(3)(10),-(root(3)(10))/(2)-(root(3)(10)sqrt3i)/(2),-(root(3)(10))/(2)+(root(3)(10)sqrt3i)/(2)}x \in \left\{ \sqrt[3]{10},\, - \frac{\sqrt[3]{10}}{2} - \frac{\sqrt[3]{10} \sqrt{3} i}{2},\, - \frac{\sqrt[3]{10}}{2} + \frac{\sqrt[3]{10} \sqrt{3} i}{2}\right\}$$x\in \{\sqrt[3]{10},-\frac{\sqrt[3]{10}}{2}-\frac{\sqrt[3]{10}\sqrt{3}i}{2},-\frac{\sqrt[3]{10}}{2}+\frac{\sqrt[3]{10}\sqrt{3}i}{2}\}$$

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  • Simplification
  $$x^3=10$$$$x^3=10$$x^(3)=10x^{3} = 10$$x^3=10$$

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System of Equations

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• Input
  $$\begin{array}{rl}4x-2y+2z& =30\\ 3x-2y-2z& =-13\\ x-y+2z& =22\end{array}$$$$\begin{array}{r}4x-2y+2z=30\\ 3x-2y-2z=-13\\ x-y+2z=22\end{array}$${:[4x-2y+2z=30],[3x-2y-2z=-13],[x-y+2z=22]:}\begin{aligned} 4 x-2 y+2 z &=30 \\ 3 x-2 y-2 z &=-13 \\ x-y+2 z &=22 \end{aligned}$$\begin{array}{rl}4x-2y+2z& =30\\ 3x-2y-2z& =-13\\ x-y+2z& =22\end{array}$$

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  • Solution
  $$\{\begin{array}{l}x=3\\ y=1\\ z=10\end{array}$$$$\left\{\begin{array}{l}x=3\\ y=1\\ z=10\end{array}\right.$${[x=3],[y=1],[z=10]:}\left\{ \begin{array} {l} \,x = 3 \\\, y = 1 \\\, z = 10 \end{array} \right.$$\{\begin{array}{l}x=3\\ y=1\\ z=10\end{array}$$

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• Input
  $$\{\begin{array}{l}0.30x+0.30y=30\\ 0.60x+0.10y=40\end{array}$$$$\left\{\begin{array}{l}0.30x+0.30y=30\\ 0.60x+0.10y=40\end{array}\right.$${[0.30 x+0.30 y=30],[0.60 x+0.10 y=40]:}\left\{\begin{array}{l}0.30 x+0.30 y=30 \\ 0.60 x+0.10 y=40\end{array}\right.$$\{\begin{array}{l}0.30x+0.30y=30\\ 0.60x+0.10y=40\end{array}$$

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  • Solution
  $$\{\begin{array}{l}x=60.0\\ y=40.0\end{array}$$$$\left\{\begin{array}{l}x=60.0\\ y=40.0\end{array}\right.$${[x=60.0],[y=40.0]:}\left\{ \begin{array} {l} \,x = 60.0 \\\, y = 40.0 \end{array} \right.$$\{\begin{array}{l}x=60.0\\ y=40.0\end{array}$$

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  • Graph
    

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• Input
  $$\{\begin{array}{r}2x+4y-z=8\\ 2x-4y+2z=3\\ x+4y+z=3\end{array}$$$$\left\{\begin{array}{r}2x+4y-z=8\\ 2x-4y+2z=3\\ x+4y+z=3\end{array}\right.$${[2x+4y-z=8],[2x-4y+2z=3],[x+4y+z=3]:}\left\{\begin{array}{r}2 x+4 y-z=8 \\ 2 x-4 y+2 z=3 \\ x+4 y+z=3\end{array}\right.$$\{\begin{array}{r}2x+4y-z=8\\ 2x-4y+2z=3\\ x+4y+z=3\end{array}$$

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  • Solution
  $$\{\begin{array}{l}x=3\\ y=\frac{1}{4}\\ z=-1\end{array}$$$$\left\{\begin{array}{l}x=3\\ y=\frac{1}{4}\\ z=-1\end{array}\right.$${[x=3],[y=(1)/(4)],[z=-1]:}\left\{ \begin{array} {l} \,x = 3 \\\, y = \frac{1}{4} \\\, z = -1 \end{array} \right.$$\{\begin{array}{l}x=3\\ y=\frac{1}{4}\\ z=-1\end{array}$$

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• Input
  $$\{\begin{array}{r}\frac{x-1}{2}+\frac{y+2}{3}=4\\ x-2y=5\end{array}$$$$\left\{\begin{array}{r}\frac{x-1}{2}+\frac{y+2}{3}=4\\ x-2y=5\end{array}\right.$${[(x-1)/(2)+(y+2)/(3)=4],[x-2y=5]:}\left\{\begin{array}{r}\frac{x-1}{2}+\frac{y+2}{3}=4 \\ x-2 y=5\end{array}\right.$$\{\begin{array}{r}\frac{x-1}{2}+\frac{y+2}{3}=4\\ x-2y=5\end{array}$$

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  • Solution
  $$\{\begin{array}{l}x=7\\ y=1\end{array}$$$$\left\{\begin{array}{l}x=7\\ y=1\end{array}\right.$${[x=7],[y=1]:}\left\{ \begin{array} {l} \,x = 7 \\\, y = 1 \end{array} \right.$$\{\begin{array}{l}x=7\\ y=1\end{array}$$

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  • Graph
    

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• Input
  $$\begin{array}{rl}2x-y& =5\\ 7x-3y& =20\end{array}$$$$\begin{array}{r}2x-y=5\\ 7x-3y=20\end{array}$${:[2x-y=5],[7x-3y=20]:}\begin{aligned} 2 x-y &=5 \\ 7 x-3 y &=20 \end{aligned}$$\begin{array}{rl}2x-y& =5\\ 7x-3y& =20\end{array}$$

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  • Solution
  $$\{\begin{array}{l}x=5\\ y=5\end{array}$$$$\left\{\begin{array}{l}x=5\\ y=5\end{array}\right.$${[x=5],[y=5]:}\left\{ \begin{array} {l} \,x = 5 \\\, y = 5 \end{array} \right.$$\{\begin{array}{l}x=5\\ y=5\end{array}$$

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  • Graph
    

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• Input
  $$x+5y=20,-3x-5y=-20$$$$x+5y=20,-3x-5y=-20$$x+5y=20,-3x-5y=-20x+5 y=20, -3 x-5 y=-20$$x+5y=20,-3x-5y=-20$$

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  • Solution
  $$\{\begin{array}{l}x=0\\ y=4\end{array}$$$$\left\{\begin{array}{l}x=0\\ y=4\end{array}\right.$${[x=0],[y=4]:}\left\{ \begin{array} {l} \,x = 0 \\\, y = 4 \end{array} \right.$$\{\begin{array}{l}x=0\\ y=4\end{array}$$

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  • Graph
    

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• Input
  $$2x+y+7z=4,3x-9y-z=2,x-8y-6z=-9$$$$2x+y+7z=4,3x-9y-z=2,x-8y-6z=-9$$2x+y+7z=4,3x-9y-z=2,x-8y-6z=-92 x+y+7 z=4, 3 x-9 y-z=2, x-8 y-6 z=-9$$2x+y+7z=4,3x-9y-z=2,x-8y-6z=-9$$

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  • Solution
  $$\{\begin{array}{l}x=-\frac{237}{2}\\ y=-\frac{177}{4}\\ z=\frac{163}{4}\end{array}$$$$\left\{\begin{array}{l}x=-\frac{237}{2}\\ y=-\frac{177}{4}\\ z=\frac{163}{4}\end{array}\right.$${[x=-(237)/(2)],[y=-(177)/(4)],[z=(163)/(4)]:}\left\{ \begin{array} {l} \,x = - \frac{237}{2} \\\, y = - \frac{177}{4} \\\, z = \frac{163}{4} \end{array} \right.$$\{\begin{array}{l}x=-\frac{237}{2}\\ y=-\frac{177}{4}\\ z=\frac{163}{4}\end{array}$$

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• Input
  $$x+y-z=-7,3x-y+z=-1,x-2y+4z=46$$$$x+y-z=-7,3x-y+z=-1,x-2y+4z=46$$x+y-z=-7,3x-y+z=-1,x-2y+4z=46x+y-z=-7, 3 x-y+z=-1, x-2 y+4 z=46$$x+y-z=-7,3x-y+z=-1,x-2y+4z=46$$

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  • Solution
  $$\{\begin{array}{l}x=-2\\ y=14\\ z=19\end{array}$$$$\left\{\begin{array}{l}x=-2\\ y=14\\ z=19\end{array}\right.$${[x=-2],[y=14],[z=19]:}\left\{ \begin{array} {l} \,x = -2 \\\, y = 14 \\\, z = 19 \end{array} \right.$$\{\begin{array}{l}x=-2\\ y=14\\ z=19\end{array}$$

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• Input
  $$x+y=10,x^2+2=y$$$$x+y=10,x^2+2=y$$x+y=10,x^(2)+2=yx + y = 10, x^2 + 2 = y$$x+y=10,x^2+2=y$$

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  • Solution
  $$\{\begin{array}{l}x=-\frac{1}{2}+\frac{\sqrt{33}}{2},y=\frac{21}{2}-\frac{\sqrt{33}}{2}\\ x=-\frac{\sqrt{33}}{2}-\frac{1}{2},y=\frac{\sqrt{33}}{2}+\frac{21}{2}\end{array}$$$$\left\{\begin{array}{l}x=-\frac{1}{2}+\frac{\sqrt{33}}{2},y=\frac{21}{2}-\frac{\sqrt{33}}{2}\\ x=-\frac{\sqrt{33}}{2}-\frac{1}{2},y=\frac{\sqrt{33}}{2}+\frac{21}{2}\end{array}\right.$${[x=-(1)/(2)+(sqrt33)/(2)","quad y=(21)/(2)-(sqrt33)/(2)],[x=-(sqrt33)/(2)-(1)/(2)","quad y=(sqrt33)/(2)+(21)/(2)]:}\left\{ \begin{array} {l} \,x = - \frac{1}{2} + \frac{\sqrt{33}}{2}\,,\quad y = \frac{21}{2} - \frac{\sqrt{33}}{2} \\\, x = - \frac{\sqrt{33}}{2} - \frac{1}{2}\,,\quad y = \frac{\sqrt{33}}{2} + \frac{21}{2} \end{array} \right.$$\{\begin{array}{l}x=-\frac{1}{2}+\frac{\sqrt{33}}{2},y=\frac{21}{2}-\frac{\sqrt{33}}{2}\\ x=-\frac{\sqrt{33}}{2}-\frac{1}{2},y=\frac{\sqrt{33}}{2}+\frac{21}{2}\end{array}$$

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  • Graph
    

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• Input
  $$\begin{array}{rl}-12x+9y& =7\\ 9x-12y& =6\end{array}$$$$\begin{array}{r}-12x+9y=7\\ 9x-12y=6\end{array}$${:[-12 x+9y=7],[9x-12 y=6]:}\begin{aligned} -12 x+9 y &=7 \\ 9 x-12 y &=6 \end{aligned}$$\begin{array}{rl}-12x+9y& =7\\ 9x-12y& =6\end{array}$$

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  • Solution
  $$\{\begin{array}{l}x=-\frac{46}{21}\\ y=-\frac{15}{7}\end{array}$$$$\left\{\begin{array}{l}x=-\frac{46}{21}\\ y=-\frac{15}{7}\end{array}\right.$${[x=-(46)/(21)],[y=-(15)/(7)]:}\left\{ \begin{array} {l} \,x = - \frac{46}{21} \\\, y = - \frac{15}{7} \end{array} \right.$$\{\begin{array}{l}x=-\frac{46}{21}\\ y=-\frac{15}{7}\end{array}$$

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  • Graph
    

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• Input
  $$\begin{array}{c}2x-y=5\\ 7x-3y=20\end{array}$$$$\begin{array}{c}2x-y=5\\ 7x-3y=20\end{array}$${:[2x-y=5],[7x-3y=20]:}\begin{array}{c} 2 x-y=5 \\ 7 x-3 y=20 \end{array}$$\begin{array}{c}2x-y=5\\ 7x-3y=20\end{array}$$

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  • Solution
  $$\{\begin{array}{l}x=5\\ y=5\end{array}$$$$\left\{\begin{array}{l}x=5\\ y=5\end{array}\right.$${[x=5],[y=5]:}\left\{ \begin{array} {l} \,x = 5 \\\, y = 5 \end{array} \right.$$\{\begin{array}{l}x=5\\ y=5\end{array}$$

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  • Graph
    

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• Input
  $$\{\begin{array}{l}2x+5\\ x^2+2\end{array}$$$$\left\{\begin{array}{l}2x+5\\ x^2+2\end{array}\right.$${[2x+5],[x^(2)+2]:}\left\{\begin{array}{l} 2 x+5 \\ x^{2}+2 \end{array}\right.$$\{\begin{array}{l}2x+5\\ x^2+2\end{array}$$

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  • Solution
  $$\mathrm{\varnothing }$$$$\mathrm{\varnothing }$$O/\emptyset$$\mathrm{\varnothing }$$

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• Input
  $$\{\begin{array}{c}{x}^3=y\\ x^2+y^2=10\\ y=2x\end{array}$$$$\left\{\begin{array}{c}{x}^3=y\\ x^2+y^2=10\\ y=2x\end{array}\right.$${[x^(3)=y],[x^(2)+y^(2)=10],[y=2x]:}\left\{\begin{array}{ccc} x^3 = y \\ x^2 + y^2 = 10 \\ y = 2x \end{array}\right.$$\{\begin{array}{c}{x}^3=y\\ x^2+y^2=10\\ y=2x\end{array}$$

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  • Solution
  $$\{\begin{array}{l}x=-\sqrt{2},y=-2\sqrt{2}\\ x=\sqrt{2},y=2\sqrt{2}\end{array}$$$$\left\{\begin{array}{l}x=-\sqrt{2},y=-2\sqrt{2}\\ x=\sqrt{2},y=2\sqrt{2}\end{array}\right.$${[x=-sqrt2","quad y=-2sqrt2],[x=sqrt2","quad y=2sqrt2]:}\left\{ \begin{array} {l} \,x = - \sqrt{2}\,,\quad y = - 2 \sqrt{2} \\\, x = \sqrt{2}\,,\quad y = 2 \sqrt{2} \end{array} \right.$$\{\begin{array}{l}x=-\sqrt{2},y=-2\sqrt{2}\\ x=\sqrt{2},y=2\sqrt{2}\end{array}$$

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  • Graph
    

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• Input
  $$\{\begin{array}{c}{x}^3=y\\ x^2+y^2=10\\ y=\sqrt{x}\end{array}$$$$\left\{\begin{array}{c}{x}^3=y\\ x^2+y^2=10\\ y=\sqrt{x}\end{array}\right.$${[x^(3)=y],[x^(2)+y^(2)=10],[y=sqrtx]:}\left\{\begin{array}{ccc} x^3 = y \\ x^2 + y^2 = 10 \\ y = \sqrt{x} \end{array}\right.$$\{\begin{array}{c}{x}^3=y\\ x^2+y^2=10\\ y=\sqrt{x}\end{array}$$

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  • Solution
  $$\mathrm{\varnothing }$$$$\mathrm{\varnothing }$$O/\emptyset$$\mathrm{\varnothing }$$

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  • Graph
    

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• Input
  $$\{\begin{array}{c}{x}^2+y=10\\ y=5x\end{array}$$$$\left\{\begin{array}{c}{x}^2+y=10\\ y=5x\end{array}\right.$${[x^(2)+y=10],[y=5x]:}\left\{ \begin{array}{ccc} x^2 + y= 10 \\y = 5x\end{array}\right.$$\{\begin{array}{c}{x}^2+y=10\\ y=5x\end{array}$$

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  • Solution
  $$\{\begin{array}{l}x=-\frac{5}{2}+\frac{\sqrt{65}}{2},y=-\frac{25}{2}+\frac{5\sqrt{65}}{2}\\ x=-\frac{\sqrt{65}}{2}-\frac{5}{2},y=-\frac{5\sqrt{65}}{2}-\frac{25}{2}\end{array}$$$$\left\{\begin{array}{l}x=-\frac{5}{2}+\frac{\sqrt{65}}{2},y=-\frac{25}{2}+\frac{5\sqrt{65}}{2}\\ x=-\frac{\sqrt{65}}{2}-\frac{5}{2},y=-\frac{5\sqrt{65}}{2}-\frac{25}{2}\end{array}\right.$${[x=-(5)/(2)+(sqrt65)/(2)","quad y=-(25)/(2)+(5sqrt65)/(2)],[x=-(sqrt65)/(2)-(5)/(2)","quad y=-(5sqrt65)/(2)-(25)/(2)]:}\left\{ \begin{array} {l} \,x = - \frac{5}{2} + \frac{\sqrt{65}}{2}\,,\quad y = - \frac{25}{2} + \frac{5 \sqrt{65}}{2} \\\, x = - \frac{\sqrt{65}}{2} - \frac{5}{2}\,,\quad y = - \frac{5 \sqrt{65}}{2} - \frac{25}{2} \end{array} \right.$$\{\begin{array}{l}x=-\frac{5}{2}+\frac{\sqrt{65}}{2},y=-\frac{25}{2}+\frac{5\sqrt{65}}{2}\\ x=-\frac{\sqrt{65}}{2}-\frac{5}{2},y=-\frac{5\sqrt{65}}{2}-\frac{25}{2}\end{array}$$

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  • Graph
    

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Limits

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• Input
  $$\underset{x\to 256}{lim}(\frac{1}{\sqrt{x}-16}-\frac{32}{x-256})=$$$$\underset{x\to 256}{lim} \left(\frac{1}{\sqrt{x}-16}-\frac{32}{x-256}\right)=$$lim_(x rarr256)((1)/(sqrtx-16)-(32)/(x-256))=\lim _{x \rightarrow 256}\left(\frac{1}{\sqrt{x}-16}-\frac{32}{x-256}\right)=$$\underset{x\to 256}{lim}(\frac{1}{\sqrt{x}-16}-\frac{32}{x-256})=$$

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  • Result
  $$\frac{1}{32}$$$$\frac{1}{32}$$(1)/(32)\frac{1}{32}$$\frac{1}{32}$$

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• Input
  $$\underset{v\to c}{lim}{L}_o\sqrt{1-\frac{v^2}{c^2}}$$$$\underset{v\to c}{lim} L_o\sqrt{1-\frac{v^2}{c^2}}$$lim_(v rarr c)L_(o)sqrt(1-(v^(2))/(c^(2)))\lim _{v \rightarrow c} L_{o} \sqrt{1-\frac{v^{2}}{c^{2}}}$$\underset{v\to c}{lim}{L}_o\sqrt{1-\frac{v^2}{c^2}}$$

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  • Result
  $$0$$$$0$$00$$0$$

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Function

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• Input
  $$f(x)=x^{3/2}+x^{2/3},\text{solve for}{f}^{\prime }(1)$$$$f(x)=x^{3/2}+x^{2/3},\text{ solve for }{f}^{\prime }(1)$$f(x)=x^(3//2)+x^(2//3)," solve for "f^(')(1)f(x)=x^{3 / 2}+x^{2 / 3}, \text { solve for } f^{\prime}(1)$$f(x)=x^{3/2}+x^{2/3},\text{ solve for }{f}^{\prime }(1)$$

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  • Solution
  $${\frac{d}{dx}f\left(x\right)|}_{\begin{array}{c}x=1\end{array}}=\frac{13}{6}$$$${\left.\frac{d}{dx}f\left(x\right)\right|}_{\begin{array}{c}x=1\end{array}}=\frac{13}{6}$$(d)/(dx)f((x))|_({:x=1:})=(13)/(6)\left. \frac{d}{d x} f{\left(x \right)} \right|_{\substack{ x=1 }} = \frac{13}{6}$${\frac{d}{dx}f\left(x\right)|}_{\begin{array}{c}x=1\end{array}}=\frac{13}{6}$$

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  • Simplification
  $$f\left(x\right)=x^{\frac{2}{3}}+x^{\frac{3}{2}}$$$$f\left(x\right)=x^{\frac{2}{3}}+x^{\frac{3}{2}}$$f(x)=x^((2)/(3))+x^((3)/(2))f{\left(x \right)} = x^{\frac{2}{3}} + x^{\frac{3}{2}}$$f\left(x\right)=x^{\frac{2}{3}}+x^{\frac{3}{2}}$$

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• Input
  $$f(x)=x^2-x-1,\text{solve for}{f}^{\prime }(x)$$$$f(x)=x^2-x-1,\text{ solve for }{f}^{\prime }(x)$$f(x)=x^(2)-x-1," solve for "f^(')(x)f(x)=x^{2}-x-1, \text { solve for } f^{\prime}(x)$$f(x)=x^2-x-1,\text{ solve for }{f}^{\prime }(x)$$

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  • Solution
  $$\frac{d}{dx}f\left(x\right)=2x-1$$$$\frac{d}{dx}f\left(x\right)=2x-1$$(d)/(dx)f(x)=2x-1\frac{d}{d x} f{\left(x \right)} = 2 x - 1$$\frac{d}{dx}f\left(x\right)=2x-1$$

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  • Simplification
  $$f\left(x\right)=x^2-x-1$$$$f\left(x\right)=x^2-x-1$$f(x)=x^(2)-x-1f{\left(x \right)} = x^{2} - x - 1$$f\left(x\right)=x^2-x-1$$

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Derivatives

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• Input
  $$\frac{d}{dx}\left[\frac{4e^x+7e^{-x}}{9}\right]$$$$\frac{d}{dx}\left[\frac{4e^x+7e^{-x}}{9}\right]$$(d)/(dx)[(4e^(x)+7e^(-x))/(9)]\frac{d}{d x}\left[\frac{4 e^{x}+7 e^{-x}}{9}\right]$$\frac{d}{dx}\left[\frac{4e^x+7e^{-x}}{9}\right]$$

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  • Result
  $$\frac{4e^x}{9}-\frac{7e^{-x}}{9}$$$$\frac{4e^x}{9}-\frac{7e^{-x}}{9}$$(4e^(x))/(9)-(7e^(-x))/(9)\frac{4 e^{x}}{9} - \frac{7 e^{- x}}{9}$$\frac{4e^x}{9}-\frac{7e^{-x}}{9}$$

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  • Simplification
  $$-(\frac{4e^{2x}}{9}+\frac{7}{9})e^{-x}+\frac{8e^x}{9}$$$$-\left(\frac{4e^{2x}}{9}+\frac{7}{9}\right)e^{-x}+\frac{8e^x}{9}$$-((4e^(2x))/(9)+(7)/(9))e^(-x)+(8e^(x))/(9)- \left(\frac{4 e^{2 x}}{9} + \frac{7}{9}\right) e^{- x} + \frac{8 e^{x}}{9}$$-(\frac{4e^{2x}}{9}+\frac{7}{9})e^{-x}+\frac{8e^x}{9}$$

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Elementary

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• Input
  $$\sin (x)$$$$\sin (x)$$sin(x)\sin(x)$$\sin (x)$$

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  • Result
  $$\sin \left(x\right)$$$$\sin \left(x\right)$$sin (x)\sin{\left(x \right)}$$\sin \left(x\right)$$

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  • Alternative Forms
  $$\{\begin{array}{l}\frac{1}{\sec (x-\frac{\pi }{2})}\\ \frac{1}{\csc \left(x\right)}\\ \frac{2\cot \left(\frac{x}{2}\right)}{{\cot }^2\left(\frac{x}{2}\right)+1}\\ \frac{2\tan \left(\frac{x}{2}\right)}{{\tan }^2\left(\frac{x}{2}\right)+1}\\ \cos (x-\frac{\pi }{2})\end{array}$$$$\left\{\begin{array}{l}\frac{1}{\sec \left(x-\frac{\pi }{2}\right)}\\ \frac{1}{\csc \left(x\right)}\\ \frac{2\cot \left(\frac{x}{2}\right)}{{\cot }^2\left(\frac{x}{2}\right)+1}\\ \frac{2\tan \left(\frac{x}{2}\right)}{{\tan }^2\left(\frac{x}{2}\right)+1}\\ \cos \left(x-\frac{\pi }{2}\right)\end{array}\right.$${[(1)/(sec ((x-(pi)/(2))))],[(1)/(csc ((x)))],[(2cot (((x)/(2))))/(cot^(2)(((x)/(2)))+1)],[(2tan (((x)/(2))))/(tan^(2)(((x)/(2)))+1)],[cos (x-(pi)/(2))]:}\left\{ \begin{array} {l} \,\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}} \\\, \frac{1}{\csc{\left(x \right)}} \\\, \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} \\\, \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} \\\, \cos{\left(x - \frac{\pi}{2} \right)} \end{array} \right.$$\{\begin{array}{l}\frac{1}{\sec (x-\frac{\pi }{2})}\\ \frac{1}{\csc \left(x\right)}\\ \frac{2\cot \left(\frac{x}{2}\right)}{{\cot }^2\left(\frac{x}{2}\right)+1}\\ \frac{2\tan \left(\frac{x}{2}\right)}{{\tan }^2\left(\frac{x}{2}\right)+1}\\ \cos (x-\frac{\pi }{2})\end{array}$$

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  • Graph
    

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Numericals

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• Input
  $$\left|\begin{array}{llll}2& 0& 2& 4\\ 3& 3& 1& 2\\ 0& 1& 3& 1\\ 4& 1& 7& 1\end{array}\right|$$$$\left|\begin{array}{l}2\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}0\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}2\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}4\\ 3\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}3\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}1\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}2\\ 0\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}1\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}3\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}1\\ 4\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}1\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}7\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}1\end{array}\right|$$|[2,0,2,4],[3,3,1,2],[0,1,3,1],[4,1,7,1]|\left|\begin{array}{llll}2 & 0 & 2 & 4 \\ 3 & 3 & 1 & 2 \\ 0 & 1 & 3 & 1 \\ 4 & 1 & 7 & 1\end{array}\right|$$\left|\begin{array}{llll}2& 0& 2& 4\\ 3& 3& 1& 2\\ 0& 1& 3& 1\\ 4& 1& 7& 1\end{array}\right|$$

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  • Result
  $$-176.0$$$$-176.0$$-176.0-176.0$$-176.0$$

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