Optimal. Leaf size=26 \[ 3 \left (2 x-\left (-1+e^{2 x-e^x x}-x\right ) x\right ) \]
________________________________________________________________________________________
Rubi [F] time = 0.51, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int e^{-e^x x} \left (e^{2 x} (-3-6 x)+e^{e^x x} (9+6 x)+e^{3 x} \left (3 x+3 x^2\right )\right ) \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (3 e^{3 x-e^x x} x (1+x)-3 e^{2 x-e^x x} (1+2 x)+3 (3+2 x)\right ) \, dx\\ &=\frac {3}{4} (3+2 x)^2+3 \int e^{3 x-e^x x} x (1+x) \, dx-3 \int e^{2 x-e^x x} (1+2 x) \, dx\\ &=\frac {3}{4} (3+2 x)^2-3 \int \left (e^{2 x-e^x x}+2 e^{2 x-e^x x} x\right ) \, dx+3 \int \left (e^{3 x-e^x x} x+e^{3 x-e^x x} x^2\right ) \, dx\\ &=\frac {3}{4} (3+2 x)^2-3 \int e^{2 x-e^x x} \, dx+3 \int e^{3 x-e^x x} x \, dx+3 \int e^{3 x-e^x x} x^2 \, dx-6 \int e^{2 x-e^x x} x \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.29, size = 18, normalized size = 0.69 \begin {gather*} 3 x \left (3-e^{-\left (\left (-2+e^x\right ) x\right )}+x\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.62, size = 29, normalized size = 1.12 \begin {gather*} 3 \, {\left ({\left (x^{2} + 3 \, x\right )} e^{\left (x e^{x}\right )} - x e^{\left (2 \, x\right )}\right )} e^{\left (-x e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int 3 \, {\left ({\left (2 \, x + 3\right )} e^{\left (x e^{x}\right )} + {\left (x^{2} + x\right )} e^{\left (3 \, x\right )} - {\left (2 \, x + 1\right )} e^{\left (2 \, x\right )}\right )} e^{\left (-x e^{x}\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.05, size = 21, normalized size = 0.81
method | result | size |
risch | \(3 x^{2}+9 x -3 x \,{\mathrm e}^{-x \left ({\mathrm e}^{x}-2\right )}\) | \(21\) |
norman | \(\left (-3 x \,{\mathrm e}^{2 x}+3 x^{2} {\mathrm e}^{{\mathrm e}^{x} x}+9 \,{\mathrm e}^{{\mathrm e}^{x} x} x \right ) {\mathrm e}^{-{\mathrm e}^{x} x}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.47, size = 22, normalized size = 0.85 \begin {gather*} 3 \, x^{2} - 3 \, x e^{\left (-x e^{x} + 2 \, x\right )} + 9 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 4.06, size = 18, normalized size = 0.69 \begin {gather*} 3\,x\,\left (x-{\mathrm {e}}^{2\,x-x\,{\mathrm {e}}^x}+3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.20, size = 22, normalized size = 0.85 \begin {gather*} 3 x^{2} - 3 x e^{2 x} e^{- x e^{x}} + 9 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________