The solver takes in inputs in the form of $L\phantom{\rule{-.325em}{0ex}}A\phantom{\rule{-.17em}{0ex}}T\phantom{\rule{-.14em}{0ex}}E\phantom{\rule{-.115em}{0ex}}X$$L\phantom{\rule{-.325em}{0ex}}A\phantom{\rule{-.17em}{0ex}}T\phantom{\rule{-.14em}{0ex}}E\phantom{\rule{-.115em}{0ex}}X$L"A"T"E"X\LaTeX expressions and
gives you an appropriate result based on the $L\phantom{\rule{-.325em}{0ex}}A\phantom{\rule{-.17em}{0ex}}T\phantom{\rule{-.14em}{0ex}}E\phantom{\rule{-.115em}{0ex}}X$$L\phantom{\rule{-.325em}{0ex}}A\phantom{\rule{-.17em}{0ex}}T\phantom{\rule{-.14em}{0ex}}E\phantom{\rule{-.115em}{0ex}}X$L"A"T"E"X\LaTeX query.
• Currently, the supported Result types are:

• 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
Examples of queries and their corresponding outputs are given below.

# Array

• Input
$\left\{\begin{array}{ll}x& x\ge 0\\ \left({e}^{x}-1\right)& x<0\end{array}$$\left\{\begin{array}{l}x x\ge 0\\ \left({e}^{x}-1\right) 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.

• 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

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

• Simplification
$\int \frac{{x}^{4}+7}{x\left({x}^{2}+5\right)}\phantom{\rule{thinmathspace}{0ex}}dx$$\int \frac{{x}^{4}+7}{x\left({x}^{2}+5\right)}\phantom{\rule{thinmathspace}{0ex}}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

• 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

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

• Result
$\frac{\left(56x-8\right){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}

• Simplification
$\frac{8\left(7x-1\right){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}{\left(x-1\right)\left(x-2\right)}dx$$\int \frac{x-3}{\left(x-1\right)\left(x-2\right)}dx$int(x-3)/((x-1)(x-2))dx\int \frac{x-3}{(x-1)(x-2)} d x

• Result
$-\mathrm{ln}\left(x-2\right)+2\mathrm{ln}\left(x-1\right)$$-\mathrm{ln}\left(x-2\right)+2\mathrm{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}{\left(x-2\right)\left(x-1\right)}\phantom{\rule{thinmathspace}{0ex}}dx$$\int \frac{x-3}{\left(x-2\right)\left(x-1\right)}\phantom{\rule{thinmathspace}{0ex}}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

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

• Simplification
$\int \frac{x}{\sqrt{2-{x}^{2}}}\phantom{\rule{thinmathspace}{0ex}}dx$$\int \frac{x}{\sqrt{2-{x}^{2}}}\phantom{\rule{thinmathspace}{0ex}}dx$int(x)/(sqrt(2-x^(2)))dx\int \frac{x}{\sqrt{2 - x^{2}}}\, dx

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

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

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

• Simplification
$\underset{0}{\overset{1}{\int }}\underset{0}{\overset{1-{x}^{2}}{\int }}\underset{3}{\overset{-{x}^{2}-y+4}{\int }}x\phantom{\rule{thinmathspace}{0ex}}dz\phantom{\rule{thinmathspace}{0ex}}dy\phantom{\rule{thinmathspace}{0ex}}dx$$\underset{0}{\overset{1}{\int }} \underset{0}{\overset{1-{x}^{2}}{\int }} \underset{3}{\overset{-{x}^{2}-y+4}{\int }} x\phantom{\rule{thinmathspace}{0ex}}dz\phantom{\rule{thinmathspace}{0ex}}dy\phantom{\rule{thinmathspace}{0ex}}dx$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=

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

• Simplification
$\int \frac{1}{2\mathrm{cosh}\left(x\right)}\phantom{\rule{thinmathspace}{0ex}}dx$$\int \frac{1}{2\mathrm{cosh}\left(x\right)}\phantom{\rule{thinmathspace}{0ex}}dx$int(1)/(2cosh ((x)))dx\int \frac{1}{2 \cosh{\left(x \right)}}\, dx

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

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

• Simplification
$\int \left(\frac{4}{3y}+\frac{3}{{y}^{2}}-\frac{2}{\sqrt[7]{y}}\right)\phantom{\rule{thinmathspace}{0ex}}dy$$\int \left(\frac{4}{3y}+\frac{3}{{y}^{2}}-\frac{2}{\sqrt[7]{y}}\right)\phantom{\rule{thinmathspace}{0ex}}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

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

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

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

• 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 7\\ 3 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]

• 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]

• 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]

• Determinant
$784$$784$784784

• Eigenvectors
$\left\{\begin{array}{l}\phantom{\rule{thinmathspace}{0ex}}{v}_{{\lambda }_{1}}=\left[\begin{array}{c}-\frac{42}{-24+6\sqrt{37}}\\ 1\end{array}\right]\\ \phantom{\rule{thinmathspace}{0ex}}{v}_{{\lambda }_{2}}=\left[\begin{array}{c}-\frac{42}{-6\sqrt{37}-24}\\ 1\end{array}\right]\end{array}$$\left\{\begin{array}{l}\phantom{\rule{thinmathspace}{0ex}}{v}_{{\lambda }_{1}}=\left[\begin{array}{c}-\frac{42}{-24+6\sqrt{37}}\\ 1\end{array}\right]\\ \phantom{\rule{thinmathspace}{0ex}}{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.

• Eigenvalues
$\left\{\begin{array}{l}\phantom{\rule{thinmathspace}{0ex}}{\lambda }_{1}=46-6\sqrt{37}\\ \phantom{\rule{thinmathspace}{0ex}}{\lambda }_{2}=6\sqrt{37}+46\end{array}$$\left\{\begin{array}{l}\phantom{\rule{thinmathspace}{0ex}}{\lambda }_{1}=46-6\sqrt{37}\\ \phantom{\rule{thinmathspace}{0ex}}{\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.

• 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

• Dimensions
$\left(2,\text{}2\right)$$\left(2,\text{}2\right)$(2,2)\left( 2, \ 2\right)

• Multiplicities
$\left\{\begin{array}{l}\phantom{\rule{thinmathspace}{0ex}}{\mu }_{A}\left({\lambda }_{1}\right)=1\\ \phantom{\rule{thinmathspace}{0ex}}{\mu }_{A}\left({\lambda }_{2}\right)=1\end{array}$$\left\{\begin{array}{l}\phantom{\rule{thinmathspace}{0ex}}{\mu }_{A}\left({\lambda }_{1}\right)=1\\ \phantom{\rule{thinmathspace}{0ex}}{\mu }_{A}\left({\lambda }_{2}\right)=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 -5 -3\\ 1 3 5\end{array}\right]+\left[\begin{array}{r}3 1 0\\ -2 6 -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]

• 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]

• 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}\mathrm{cos}\theta & \mathrm{sin}\theta \\ -\mathrm{sin}\theta & \mathrm{cos}\theta \end{array}\right)$$\left(\begin{array}{cc}\mathrm{cos}\theta & \mathrm{sin}\theta \\ -\mathrm{sin}\theta & \mathrm{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)

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

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

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

• Eigenvectors
$\left\{\begin{array}{l}\phantom{\rule{thinmathspace}{0ex}}{v}_{{\lambda }_{1}}=\left[\begin{array}{c}-\frac{\mathrm{sin}\left(\theta \right)}{\sqrt{\left(\mathrm{cos}\left(\theta \right)-1\right)\left(\mathrm{cos}\left(\theta \right)+1\right)}}\\ 1\end{array}\right]\\ \phantom{\rule{thinmathspace}{0ex}}{v}_{{\lambda }_{2}}=\left[\begin{array}{c}\frac{\mathrm{sin}\left(\theta \right)}{\sqrt{\left(\mathrm{cos}\left(\theta \right)-1\right)\left(\mathrm{cos}\left(\theta \right)+1\right)}}\\ 1\end{array}\right]\end{array}$$\left\{\begin{array}{l}\phantom{\rule{thinmathspace}{0ex}}{v}_{{\lambda }_{1}}=\left[\begin{array}{c}-\frac{\mathrm{sin}\left(\theta \right)}{\sqrt{\left(\mathrm{cos}\left(\theta \right)-1\right)\left(\mathrm{cos}\left(\theta \right)+1\right)}}\\ 1\end{array}\right]\\ \phantom{\rule{thinmathspace}{0ex}}{v}_{{\lambda }_{2}}=\left[\begin{array}{c}\frac{\mathrm{sin}\left(\theta \right)}{\sqrt{\left(\mathrm{cos}\left(\theta \right)-1\right)\left(\mathrm{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.

• Eigenvalues
$\left\{\begin{array}{l}\phantom{\rule{thinmathspace}{0ex}}{\lambda }_{1}=-\sqrt{\left(\mathrm{cos}\left(\theta \right)-1\right)\left(\mathrm{cos}\left(\theta \right)+1\right)}+\mathrm{cos}\left(\theta \right)\\ \phantom{\rule{thinmathspace}{0ex}}{\lambda }_{2}=\sqrt{\left(\mathrm{cos}\left(\theta \right)-1\right)\left(\mathrm{cos}\left(\theta \right)+1\right)}+\mathrm{cos}\left(\theta \right)\end{array}$$\left\{\begin{array}{l}\phantom{\rule{thinmathspace}{0ex}}{\lambda }_{1}=-\sqrt{\left(\mathrm{cos}\left(\theta \right)-1\right)\left(\mathrm{cos}\left(\theta \right)+1\right)}+\mathrm{cos}\left(\theta \right)\\ \phantom{\rule{thinmathspace}{0ex}}{\lambda }_{2}=\sqrt{\left(\mathrm{cos}\left(\theta \right)-1\right)\left(\mathrm{cos}\left(\theta \right)+1\right)}+\mathrm{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.

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

• Dimensions
$\left(2,\text{}2\right)$$\left(2,\text{}2\right)$(2,2)\left( 2, \ 2\right)

• Multiplicities
$\left\{\begin{array}{l}\phantom{\rule{thinmathspace}{0ex}}{\mu }_{A}\left({\lambda }_{1}\right)=1\\ \phantom{\rule{thinmathspace}{0ex}}{\mu }_{A}\left({\lambda }_{2}\right)=1\end{array}$$\left\{\begin{array}{l}\phantom{\rule{thinmathspace}{0ex}}{\mu }_{A}\left({\lambda }_{1}\right)=1\\ \phantom{\rule{thinmathspace}{0ex}}{\mu }_{A}\left({\lambda }_{2}\right)=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
${\left(-18{m}^{2}n\right)}^{2}\ast \left(-\frac{1}{6}m{n}^{2}\right)=$${\left(-18{m}^{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)=

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

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

• Graph

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

• Result
$-1$$-1$-1-1

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

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

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

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

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

• 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}

• 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}

• Graph

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

• 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}

• 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}

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

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

• Graph

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

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

• Result
$24024$$24024$2402424024

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

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

• Numerical
$106.0$$106.0$106.0106.0

• Simplification
$106$$106$106106

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

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

• Roots
$\left\{\begin{array}{l}\phantom{\rule{thinmathspace}{0ex}}m=\frac{5x}{6}\phantom{\rule{thinmathspace}{0ex}},\phantom{\rule{1em}{0ex}}m=x\left(-\frac{5}{12}-\frac{5\sqrt{3}i}{12}\right)\phantom{\rule{thinmathspace}{0ex}},\phantom{\rule{1em}{0ex}}m=x\left(-\frac{5}{12}+\frac{5\sqrt{3}i}{12}\right)\\ \phantom{\rule{thinmathspace}{0ex}}x=\frac{6m}{5}\phantom{\rule{thinmathspace}{0ex}},\phantom{\rule{1em}{0ex}}x=6m\left(-\frac{1}{10}-\frac{\sqrt{3}i}{10}\right)\phantom{\rule{thinmathspace}{0ex}},\phantom{\rule{1em}{0ex}}x=6m\left(-\frac{1}{10}+\frac{\sqrt{3}i}{10}\right)\end{array}$$\left\{\begin{array}{l}\phantom{\rule{thinmathspace}{0ex}}m=\frac{5x}{6}\phantom{\rule{thinmathspace}{0ex}},\phantom{\rule{1em}{0ex}}m=x\left(-\frac{5}{12}-\frac{5\sqrt{3}i}{12}\right)\phantom{\rule{thinmathspace}{0ex}},\phantom{\rule{1em}{0ex}}m=x\left(-\frac{5}{12}+\frac{5\sqrt{3}i}{12}\right)\\ \phantom{\rule{thinmathspace}{0ex}}x=\frac{6m}{5}\phantom{\rule{thinmathspace}{0ex}},\phantom{\rule{1em}{0ex}}x=6m\left(-\frac{1}{10}-\frac{\sqrt{3}i}{10}\right)\phantom{\rule{thinmathspace}{0ex}},\phantom{\rule{1em}{0ex}}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.

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

• Graph

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

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

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

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

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

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

• Roots
$x\in \left\{-6,\phantom{\rule{thinmathspace}{0ex}}3\right\}$$x\in \left\{-6,\phantom{\rule{thinmathspace}{0ex}}3\right\}$x in{-6,3}x \in \left\{ -6,\, 3\right\}

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

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

• Graph

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

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

• Numerical
$0.034899496702501$$0.034899496702501$0.0348994967025010.034899496702501

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

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

• Result
$36$$36$3636

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

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