Optimal. Leaf size=29 \[ 9 e^{2 x}-e^{-x-\left (-1+e^{-x}\right ) x^2} x \]
[Out]
________________________________________________________________________________________
Rubi [F]
time = 1.16, 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^{-2 x-e^{-x} \left (x^2-e^x x^2\right )} \left (18 e^{4 x+e^{-x} \left (x^2-e^x x^2\right )}+2 x^2-x^3+e^x \left (-1+x-2 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 e^{e^{-x} x \left (-2 e^x-x+e^x x\right )} \left (18 e^{4 x+e^{-x} \left (x^2-e^x x^2\right )}+2 x^2-x^3+e^x \left (-1+x-2 x^2\right )\right ) \, dx\\ &=\int \left (18 \exp \left (4 x+\left (-1+e^{-x}\right ) x^2+e^{-x} x \left (-2 e^x-x+e^x x\right )\right )+2 e^{e^{-x} x \left (-2 e^x-x+e^x x\right )} x^2-e^{e^{-x} x \left (-2 e^x-x+e^x x\right )} x^3-e^{x+e^{-x} x \left (-2 e^x-x+e^x x\right )} \left (1-x+2 x^2\right )\right ) \, dx\\ &=2 \int e^{e^{-x} x \left (-2 e^x-x+e^x x\right )} x^2 \, dx+18 \int \exp \left (4 x+\left (-1+e^{-x}\right ) x^2+e^{-x} x \left (-2 e^x-x+e^x x\right )\right ) \, dx-\int e^{e^{-x} x \left (-2 e^x-x+e^x x\right )} x^3 \, dx-\int e^{x+e^{-x} x \left (-2 e^x-x+e^x x\right )} \left (1-x+2 x^2\right ) \, dx\\ &=2 \int e^{e^{-x} x \left (-2 e^x-x+e^x x\right )} x^2 \, dx+\frac {18 \text {Subst}\left (\int 1 \, dx,x,\exp \left (4 x+\left (-1+e^{-x}\right ) x^2+e^{-x} x \left (-2 e^x-x+e^x x\right )\right )\right )}{4+2 \left (-1+e^{-x}\right ) x-e^{-x} x^2+e^{-x} x \left (-1-e^x+e^x x\right )+e^{-x} \left (-2 e^x-x+e^x x\right )-e^{-x} x \left (-2 e^x-x+e^x x\right )}-\int e^{e^{-x} x \left (-2 e^x-x+e^x x\right )} x^3 \, dx-\int e^{e^{-x} x \left (-e^x-x+e^x x\right )} \left (1-x+2 x^2\right ) \, dx\\ &=\frac {18 \exp \left (4 x-\left (1-e^{-x}\right ) x^2-e^{-x} x \left (2 e^x+x-e^x x\right )\right )}{4-2 \left (1-e^{-x}\right ) x-e^{-x} x^2-e^{-x} x \left (1+e^x-e^x x\right )-e^{-x} \left (2 e^x+x-e^x x\right )+e^{-x} x \left (2 e^x+x-e^x x\right )}+2 \int e^{e^{-x} x \left (-2 e^x-x+e^x x\right )} x^2 \, dx-\int e^{e^{-x} x \left (-2 e^x-x+e^x x\right )} x^3 \, dx-\int \left (e^{e^{-x} x \left (-e^x-x+e^x x\right )}-e^{e^{-x} x \left (-e^x-x+e^x x\right )} x+2 e^{e^{-x} x \left (-e^x-x+e^x x\right )} x^2\right ) \, dx\\ &=\frac {18 \exp \left (4 x-\left (1-e^{-x}\right ) x^2-e^{-x} x \left (2 e^x+x-e^x x\right )\right )}{4-2 \left (1-e^{-x}\right ) x-e^{-x} x^2-e^{-x} x \left (1+e^x-e^x x\right )-e^{-x} \left (2 e^x+x-e^x x\right )+e^{-x} x \left (2 e^x+x-e^x x\right )}+2 \int e^{e^{-x} x \left (-2 e^x-x+e^x x\right )} x^2 \, dx-2 \int e^{e^{-x} x \left (-e^x-x+e^x x\right )} x^2 \, dx-\int e^{e^{-x} x \left (-e^x-x+e^x x\right )} \, dx+\int e^{e^{-x} x \left (-e^x-x+e^x x\right )} x \, dx-\int e^{e^{-x} x \left (-2 e^x-x+e^x x\right )} x^3 \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.67, size = 27, normalized size = 0.93 \begin {gather*} 9 e^{2 x}-e^{-x \left (1+\left (-1+e^{-x}\right ) x\right )} x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.11, size = 26, normalized size = 0.90
method | result | size |
risch | \(9 \,{\mathrm e}^{2 x}-x \,{\mathrm e}^{-x \left (x \,{\mathrm e}^{-x}-x +1\right )}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.37, size = 27, normalized size = 0.93 \begin {gather*} -x e^{\left (-x^{2} e^{\left (-x\right )} + x^{2} - x\right )} + 9 \, e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.38, size = 34, normalized size = 1.17 \begin {gather*} -x e^{\left (-{\left (x^{2} - {\left (x^{2} - 2 \, x\right )} e^{x}\right )} e^{\left (-x\right )} + x\right )} + 9 \, e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.10, size = 26, normalized size = 0.90 \begin {gather*} - x e^{- x} e^{- \left (- x^{2} e^{x} + x^{2}\right ) e^{- x}} + 9 e^{2 x} \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*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 1.91, size = 28, normalized size = 0.97 \begin {gather*} 9\,{\mathrm {e}}^{2\,x}-x\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{-x^2\,{\mathrm {e}}^{-x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________