The solver takes in inputs in the form of
L"A"T"E"X\LaTeX expressions and
gives you an appropriate result based on the
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
{[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(x^(4)+7)/(x^(3)+5x)dx\int \frac{x^{4}+7}{x^{3}+5 x} d x
(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}
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
(1)/(3)\frac{1}{3}
-
Input
intx^(2)e^(-2x)dx\int x^{2} e^{-2 x} d x
((-2x^(2)-2x-1)e^(-2x))/(4)\frac{\left(- 2 x^{2} - 2 x - 1\right) e^{- 2 x}}{4}
-
Input
int8xe^(7x)dx\int 8 x e^{7 x} d x
((56 x-8)e^(7x))/(49)\frac{\left(56 x - 8\right) e^{7 x}}{49}
(8(7x-1)e^(7x))/(49)\frac{8 \left(7 x - 1\right) e^{7 x}}{49}
-
Input
int(x-3)/((x-1)(x-2))dx\int \frac{x-3}{(x-1)(x-2)} d x
-ln (x-2)+2ln (x-1)- \ln{\left(x - 2 \right)} + 2 \ln{\left(x - 1 \right)}
int(x-3)/((x-2)(x-1))dx\int \frac{x - 3}{\left(x - 2\right) \left(x - 1\right)}\, dx
-
Input
int(x)/(sqrt(2-x^(2)))dx\int \frac{x}{\sqrt{2-x^{2}}} d x
-sqrt(2-x^(2))- \sqrt{2 - x^{2}}
int(x)/(sqrt(2-x^(2)))dx\int \frac{x}{\sqrt{2 - x^{2}}}\, dx
-
Input
inte^(x)cos 4xdx\int e^{x} \cos 4 x d x
(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} x d z d y d x
(1)/(12)\frac{1}{12}
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(e^(x))/(1+e^(2x))dx=\int \frac{e^{x}}{1+e^{2 x}} d x=
tan^(-1)(e^(x))\tan^{-1}{\left(e^{x} \right)}
int(1)/(2cosh ((x)))dx\int \frac{1}{2 \cosh{\left(x \right)}}\, dx
-
Input
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
-(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}
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+(1)/(u)+(1)/(u^(2))du\int_{1}^{5} 1+\frac{1}{u}+\frac{1}{u^{2}} d u
ln (5)+(24)/(5)\ln{\left(5 \right)} + \frac{24}{5}
-
Input
int(-8e^(t)+19 t)dt\int\left(-8 e^{t}+19 t\right) d t
(19t^(2))/(2)-8e^(t)\frac{19 t^{2}}{2} - 8 e^{t}
-
Input
inte^(3x+9)dx\int e^{3 x+9} d x
(e^(3x+9))/(3)\frac{e^{3 x + 9}}{3}
Matrices
-
Input
[[-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]
[[22,42],[18,70]]\left[\begin{matrix}22 & 42\\18 & 70\end{matrix}\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]
{[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.
{[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(lambda)=lambda^(2)-92 lambda+784p{\left(\lambda \right)} = \lambda^{2} - 92 \lambda + 784
(2,2)\left( 2, \ 2\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
[[-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]
[[0,-4,-3],[-1,9,3]]\left[\begin{matrix}0 & -4 & -3\\-1 & 9 & 3\end{matrix}\right]
-
Input
[[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]
[[2,-1],[0,3],[-4,5]]\left[\begin{matrix}2 & -1\\0 & 3\\-4 & 5\end{matrix}\right]
-
Input
([cos theta,sin theta],[-sin theta,cos theta])\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{matrix}\cos{\left(\theta \right)} & \sin{\left(\theta \right)}\\- \sin{\left(\theta \right)} & \cos{\left(\theta \right)}\end{matrix}\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]
sin^(2)(theta)+cos^(2)(theta)\sin^{2}{\left(\theta \right)} + \cos^{2}{\left(\theta \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.
{[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(lambda)=lambda^(2)-2lambda cos (theta)+1p{\left(\lambda \right)} = \lambda^{2} - 2 \lambda \cos{\left(\theta \right)} + 1
(2,2)\left( 2, \ 2\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)**(-(1)/(6)mn^(2))=\left(-18 m^{2} n\right)^{2} *\left(-\frac{1}{6} m n^{2}\right)=
{[m=0],[n=0]:}\left\{ \begin{array} {l} \,m = 0 \\\,
n = 0 \end{array} \right.
-54m^(5)n^(4)- 54 m^{5} n^{4}
- Graph

-
Input
log_(6)(1)/(6)\log _{6} \frac{1}{6}
-
Input
(-7+6i)(3+i)(-7+6 i)(3+i)
(-7+6i)(3+i)\left(-7 + 6 i\right) \left(3 + i\right)
-27.0+11.0 i-27.0 + 11.0 i
-27+11 i-27 + 11 i
-
Input
sqrt((252q^(6)k^(16))/(175 qk^(4)))\sqrt{\frac{252 q^{6} k^{16}}{175 q k^{4}}}
(6sqrt(k^(12)q^(5)))/(5)\frac{6 \sqrt{k^{12} q^{5}}}{5}
6sqrt7(sqrt7sqrt(k^(12)q^(5)))/(35)6 \sqrt{7} \frac{\sqrt{7} \sqrt{k^{12} q^{5}}}{35}
- Graph

-
Input
(sqrt(160y^(10)))/(sqrt(2y^(2)))\frac{\sqrt{160 y^{10}}}{\sqrt{2 y^{2}}}
(4sqrt5sqrt(y^(10)))/(sqrt(y^(2)))\frac{4 \sqrt{5} \sqrt{y^{10}}}{\sqrt{y^{2}}}
- Graph

-
Input
(z)/(z^(2)+9z+14)+(2)/(z^(2)+9z+14)\frac{z}{z^{2}+9 z+14}+\frac{2}{z^{2}+9 z+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}
(1)/(z+7)\frac{1}{z + 7}
(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
(14!)/((14-4)!)\frac{14 !}{(14-4) !}
(14!)/((-4+14)!)\frac{14!}{\left(-4 + 14\right)!}
2402424024
-
Input
(5-9i)(5+9i)(5-9 i)(5+9 i)
(5-9i)(5+9i)\left(5 - 9 i\right) \left(5 + 9 i\right)
106.0106.0
-
Input
125x^(3)-216m^(3)125 x^{3}-216 m^{3}
(-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)
{[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.
-216m^(3)+125x^(3)- 216 m^{3} + 125 x^{3}
- Graph

-
Input
(5+2i)^(2)(5+2 i)^{2}
(5+2i)^(2)\left(5 + 2 i\right)^{2}
21.0+20.0 i21.0 + 20.0 i
21+20 i21 + 20 i
-
Input
x^(2)+3x-18x^{2}+3 x-18
(x-3)(x+6)\left(x - 3\right) \left(x + 6\right)
x in{-6,3}x \in \left\{ -6,\, 3\right\}
x^(2)+3x-18x^{2} + 3 x - 18
(x^(2)+3x)-18\left(x^{2} + 3 x\right) - 18
- Graph

-
Input
2cos^(2)(44^(@))-12 \cos ^{2}\left(44^{\circ}\right)-1
-1+2cos^(2)((11 pi)/(45))-1 + 2 \cos^{2}{\left(\frac{11 \pi}{45} \right)}
0.0348994967025010.034899496702501
cos ((22 pi)/(45))\cos{\left(\frac{22 \pi}{45} \right)}
-
Input
(-18)-:6xx(-12)=(-18) \div 6 \times(-12)=
-
Input
ln((e^(5))/(6))\ln \left(\frac{e^{5}}{6}\right)
ln ((e^(5))/(6))\ln{\left(\frac{e^{5}}{6} \right)}