Optimal. Leaf size=23 \[ x \left (9+x-256 x^4-\frac {5 e^{-2 e^x}}{\log (x)}\right ) \]
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Rubi [F]
time = 0.85, 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 \frac {e^{-2 e^x} \left (5+\left (-5+10 e^x x\right ) \log (x)+e^{2 e^x} \left (9+2 x-1280 x^4\right ) \log ^2(x)\right )}{\log ^2(x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {10 e^{-2 e^x+x} x}{\log (x)}-\frac {e^{-2 e^x} \left (-5+5 \log (x)-9 e^{2 e^x} \log ^2(x)-2 e^{2 e^x} x \log ^2(x)+1280 e^{2 e^x} x^4 \log ^2(x)\right )}{\log ^2(x)}\right ) \, dx\\ &=10 \int \frac {e^{-2 e^x+x} x}{\log (x)} \, dx-\int \frac {e^{-2 e^x} \left (-5+5 \log (x)-9 e^{2 e^x} \log ^2(x)-2 e^{2 e^x} x \log ^2(x)+1280 e^{2 e^x} x^4 \log ^2(x)\right )}{\log ^2(x)} \, dx\\ &=10 \int \frac {e^{-2 e^x+x} x}{\log (x)} \, dx-\int \left (-9-2 x+1280 x^4-\frac {5 e^{-2 e^x}}{\log ^2(x)}+\frac {5 e^{-2 e^x}}{\log (x)}\right ) \, dx\\ &=9 x+x^2-256 x^5+5 \int \frac {e^{-2 e^x}}{\log ^2(x)} \, dx-5 \int \frac {e^{-2 e^x}}{\log (x)} \, dx+10 \int \frac {e^{-2 e^x+x} x}{\log (x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.74, size = 23, normalized size = 1.00 \begin {gather*} x \left (9+x-256 x^4-\frac {5 e^{-2 e^x}}{\log (x)}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 25, normalized size = 1.09
method | result | size |
risch | \(-256 x^{5}+x^{2}+9 x -\frac {5 x \,{\mathrm e}^{-2 \,{\mathrm e}^{x}}}{\ln \left (x \right )}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 24, normalized size = 1.04 \begin {gather*} -256 \, x^{5} + x^{2} + 9 \, x - \frac {5 \, x e^{\left (-2 \, e^{x}\right )}}{\log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 37, normalized size = 1.61 \begin {gather*} -\frac {{\left ({\left (256 \, x^{5} - x^{2} - 9 \, x\right )} e^{\left (2 \, e^{x}\right )} \log \left (x\right ) + 5 \, x\right )} e^{\left (-2 \, e^{x}\right )}}{\log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.09, size = 24, normalized size = 1.04 \begin {gather*} - 256 x^{5} + x^{2} + 9 x - \frac {5 x e^{- 2 e^{x}}}{\log {\left (x \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 34, normalized size = 1.48 \begin {gather*} -\frac {256 \, x^{5} \log \left (x\right ) - x^{2} \log \left (x\right ) + 5 \, x e^{\left (-2 \, e^{x}\right )} - 9 \, x \log \left (x\right )}{\log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.54, size = 24, normalized size = 1.04 \begin {gather*} 9\,x+x^2-256\,x^5-\frac {5\,x\,{\mathrm {e}}^{-2\,{\mathrm {e}}^x}}{\ln \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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