The solver takes in inputs in the form of L A T E X L A T E X L"A"T"E"X\LaTeX expressions and
gives you an appropriate result based on the L A T E X L A T E X L"A"T"E"X\LaTeX query.

  • 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 x      x 0 e x 1      x < 0 {[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
      Plot

Integrals


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

    • Result
    x 2 2 + 7 ln ( x ) 5 16 ln ( x 2 + 5 ) 5 x 2 2 + 7 ln x 5 16 ln x 2 + 5 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
    x 4 + 7 x ( x 2 + 5 ) d x x 4 + 7 x x 2 + 5 d x int(x^(4)+7)/(x(x^(2)+5))dx\int \frac{x^{4} + 7}{x \left(x^{2} + 5\right)}\, dx

  • Input
    0 1 x 2 d x 0 1 x 2 d x int_(0)^(1)x^(2)dx\int_0^1 x^2 dx

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

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

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

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

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

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

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

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

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

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

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

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

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

    • Result
    4 e x sin ( 4 x ) 17 + e x cos ( 4 x ) 17 4 e x sin 4 x 17 + e x cos 4 x 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
    0 1 0 1 x 2 3 4 x 2 y x d z d y d x 0 1 0 1 x 2 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\int_{0}^{1} \int_{0}^{1-x^{2}} \int_{3}^{4-x^{2}-y} x d z d y d x

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

    • Simplification
    0 1 0 1 x 2 3 x 2 y + 4 x d z d y d x 0 1 0 1 x 2 3 x 2 y + 4 x d z d y d x 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
    e x 1 + e 2 x d x = e x 1 + e 2 x d x = int(e^(x))/(1+e^(2x))dx=\int \frac{e^{x}}{1+e^{2 x}} d x=

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

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

  • Input
    ( 4 3 y + 3 y 2 2 y 7 ) d y 4 3 y + 3 y 2 2 y 7 d 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) d y

    • Result
    7 y 6 7 3 + 4 ln ( y ) 3 3 y 7 y 6 7 3 + 4 ln y 3 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
    ( 4 3 y + 3 y 2 2 y 7 ) d y 4 3 y + 3 y 2 2 y 7 d 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
    1 5 1 + 1 u + 1 u 2 d u 1 5 1 + 1 u + 1 u 2 d u int_(1)^(5)1+(1)/(u)+(1)/(u^(2))du\int_{1}^{5} 1+\frac{1}{u}+\frac{1}{u^{2}} d u

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

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

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

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

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

Matrices


  • Input
    [ 1 7 3 7 ] [ 1 7 3 7 ] 1 7 3 7 1      7 3      7 [[-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
    [ 22 42 18 70 ] 22 42 18 70 [[22,42],[18,70]]\left[\begin{matrix}22 & 42\\18 & 70\end{matrix}\right]

    • Inverse
    [ 5 56 3 56 9 392 11 392 ] 5 56 3 56 9 392 11 392 [[(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
    { v λ 1 = [ 42 24 + 6 37 1 ] v λ 2 = [ 42 6 37 24 1 ] v λ 1 = 42 24 + 6 37 1 v λ 2 = 42 6 37 24 1 {[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
    { λ 1 = 46 6 37 λ 2 = 6 37 + 46 λ 1 = 46 6 37 λ 2 = 6 37 + 46 {[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 ( λ ) = λ 2 92 λ + 784 p λ = λ 2 92 λ + 784 p(lambda)=lambda^(2)-92 lambda+784p{\left(\lambda \right)} = \lambda^{2} - 92 \lambda + 784

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

    • Multiplicities
    { μ A ( λ 1 ) = 1 μ A ( λ 2 ) = 1 μ A ( λ 1 ) = 1 μ A ( λ 2 ) = 1 {[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 ] 3      5      3 1      3      5 + 3      1      0 2      6      2 [[-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
    [ 0 4 3 1 9 3 ] 0 4 3 1 9 3 [[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 ] 4 5 6 5 1 4 2 4 6 2 3 1 [[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
    [ 2 1 0 3 4 5 ] 2 1 0 3 4 5 [[2,-1],[0,3],[-4,5]]\left[\begin{matrix}2 & -1\\0 & 3\\-4 & 5\end{matrix}\right]

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

    • Result
    [ cos ( θ ) sin ( θ ) sin ( θ ) cos ( θ ) ] cos θ sin θ sin θ cos θ [[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
    [ 1 sin 2 ( θ ) cos ( θ ) sin ( θ ) sin ( θ ) cos ( θ ) ] 1 sin 2 θ cos θ sin θ sin θ cos θ [[(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
    sin 2 ( θ ) + cos 2 ( θ ) sin 2 θ + cos 2 θ sin^(2)(theta)+cos^(2)(theta)\sin^{2}{\left(\theta \right)} + \cos^{2}{\left(\theta \right)}

    • Eigenvectors
    { v λ 1 = [ sin ( θ ) ( cos ( θ ) 1 ) ( cos ( θ ) + 1 ) 1 ] v λ 2 = [ sin ( θ ) ( cos ( θ ) 1 ) ( cos ( θ ) + 1 ) 1 ] v λ 1 = sin θ cos θ 1 cos θ + 1 1 v λ 2 = sin θ cos θ 1 cos θ + 1 1 {[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
    { λ 1 = ( cos ( θ ) 1 ) ( cos ( θ ) + 1 ) + cos ( θ ) λ 2 = ( cos ( θ ) 1 ) ( cos ( θ ) + 1 ) + cos ( θ ) λ 1 = cos θ 1 cos θ + 1 + cos θ λ 2 = cos θ 1 cos θ + 1 + cos θ {[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 ( λ ) = λ 2 2 λ cos ( θ ) + 1 p λ = λ 2 2 λ cos θ + 1 p(lambda)=lambda^(2)-2lambda cos (theta)+1p{\left(\lambda \right)} = \lambda^{2} - 2 \lambda \cos{\left(\theta \right)} + 1

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

    • Multiplicities
    { μ A ( λ 1 ) = 1 μ A ( λ 2 ) = 1 μ A ( λ 1 ) = 1 μ A ( λ 2 ) = 1 {[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
    ( 18 m 2 n ) 2 ( 1 6 m n 2 ) = 18 m 2 n 2 1 6 m n 2 = (-18m^(2)n)^(2)**(-(1)/(6)mn^(2))=\left(-18 m^{2} n\right)^{2} *\left(-\frac{1}{6} m n^{2}\right)=

    • Roots
    { m = 0 n = 0 m = 0 n = 0 {[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
      Plot

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

    • Result
    1 1 -1-1

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

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

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

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

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

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

    • Expansion
    6 7 7 k 12 q 5 35 6 7 7 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
      Plot

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

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

    • Graph
      Plot

  • Input
    z z 2 + 9 z + 14 + 2 z 2 + 9 z + 14 z z 2 + 9 z + 14 + 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}

    • Result
    z z 2 + 9 z + 14 + 2 z 2 + 9 z + 14 z z 2 + 9 z + 14 + 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}

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

    • Expansion
    z ( z 2 + 9 z ) + 14 + 2 ( z 2 + 9 z ) + 14 z z 2 + 9 z + 14 + 2 z 2 + 9 z + 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
      Plot

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

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

    • Result
    24024 24024 2402424024

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

    • Result
    ( 5 9 i ) ( 5 + 9 i ) 5 9 i 5 + 9 i (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
    ( 6 m + 5 x ) ( 36 m 2 + 30 m x + 25 x 2 ) 6 m + 5 x 36 m 2 + 30 m x + 25 x 2 (-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
    { m = 5 x 6 , m = x ( 5 12 5 3 i 12 ) , m = x ( 5 12 + 5 3 i 12 ) x = 6 m 5 , x = 6 m ( 1 10 3 i 10 ) , x = 6 m ( 1 10 + 3 i 10 ) m = 5 x 6 , m = x 5 12 5 3 i 12 , m = x 5 12 + 5 3 i 12 x = 6 m 5 , x = 6 m 1 10 3 i 10 , x = 6 m 1 10 + 3 i 10 {[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
      Plot

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

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

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

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

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

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

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

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

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

    • Graph
      Plot

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

    • Result
    1 + 2 cos 2 ( 11 π 45 ) 1 + 2 cos 2 11 π 45 -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
    cos ( 22 π 45 ) cos 22 π 45 cos ((22 pi)/(45))\cos{\left(\frac{22 \pi}{45} \right)}

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

    • Result
    36 36 3636

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

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