The Solver:

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

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

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

Array

• 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.

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  • Graph
    

    

Integrals

• 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

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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}

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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

• 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

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

• 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

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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}

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

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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}

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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}

• 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

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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)}

  ---

  • 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

• 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

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

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

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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}

• 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

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

• 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=

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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)}

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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

• 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

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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}

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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

• 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

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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}

• 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

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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}

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

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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}

Matrices

• 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]

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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]

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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]

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

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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.

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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.

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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

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

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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.

• 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]

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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]

• 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]

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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]

• 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)

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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]

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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]

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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)}

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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.

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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.

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  • 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

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

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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.

Generic

• 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)=

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  • 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.

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

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  • Graph
    

    

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

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  • Result
  $$-1$$$$-1$$-1-1

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

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

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

• 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}}}

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  • 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}

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  • 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}

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  • 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}}}

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  • 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}}}

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  • 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}

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  • 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}

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

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  • 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}

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  • Graph
    

    

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

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

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

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

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  • 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)

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

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

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

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  • 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)

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  • 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.

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

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  • Graph