Optimal. Leaf size=31 \[ e^{\frac {25 x^2 \left (5+(i \pi +\log (3)) \left (e^x+x-\log (x)\right )\right )}{\log (2)}} \]
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Rubi [A]
time = 2.04, antiderivative size = 61, normalized size of antiderivative = 1.97, number of steps
used = 2, number of rules used = 2, integrand size = 118, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.017, Rules used = {12, 6838}
\begin {gather*} x^{-\frac {25 x^2 (\log (3)+i \pi )}{\log (2)}} \exp \left (\frac {25 \left (x^3 (\log (3)+i \pi )+5 x^2+e^x x^2 (\log (3)+i \pi )\right )}{\log (2)}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \exp \left (\frac {125 x^2+25 e^x x^2 (i \pi +\log (3))+25 x^3 (i \pi +\log (3))-25 x^2 (i \pi +\log (3)) \log (x)}{\log (2)}\right ) \left (250 x+e^x \left (50 x+25 x^2\right ) (i \pi +\log (3))+\left (-25 x+75 x^2\right ) (i \pi +\log (3))-50 x (i \pi +\log (3)) \log (x)\right ) \, dx}{\log (2)}\\ &=\exp \left (\frac {25 \left (5 x^2+e^x x^2 (i \pi +\log (3))+x^3 (i \pi +\log (3))\right )}{\log (2)}\right ) x^{-\frac {25 x^2 (i \pi +\log (3))}{\log (2)}}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 2.57, size = 55, normalized size = 1.77 \begin {gather*} e^{\frac {25 x^2 \left (5+i \pi x+x \log (3)+e^x (i \pi +\log (3))\right )}{\log (2)}} x^{-\frac {25 x^2 (i \pi +\log (3))}{\log (2)}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.88, size = 45, normalized size = 1.45
method | result | size |
risch | \({\mathrm e}^{\frac {25 x^{2} \left (-i \pi \ln \left (x \right )+i {\mathrm e}^{x} \pi +i x \pi -\ln \left (3\right ) \ln \left (x \right )+\ln \left (3\right ) {\mathrm e}^{x}+x \ln \left (3\right )+5\right )}{\ln \left (2\right )}}\) | \(45\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.73, size = 82, normalized size = 2.65 \begin {gather*} e^{\left (\frac {25 i \, \pi x^{3}}{\log \left (2\right )} + \frac {25 i \, \pi x^{2} e^{x}}{\log \left (2\right )} + \frac {25 \, x^{3} \log \left (3\right )}{\log \left (2\right )} + \frac {25 \, x^{2} e^{x} \log \left (3\right )}{\log \left (2\right )} - \frac {25 i \, \pi x^{2} \log \left (x\right )}{\log \left (2\right )} - \frac {25 \, x^{2} \log \left (3\right ) \log \left (x\right )}{\log \left (2\right )} + \frac {125 \, x^{2}}{\log \left (2\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 82, normalized size = 2.65 \begin {gather*} e^{\left (\frac {25 i \, \pi x^{3}}{\log \left (2\right )} + \frac {25 i \, \pi x^{2} e^{x}}{\log \left (2\right )} + \frac {25 \, x^{3} \log \left (3\right )}{\log \left (2\right )} + \frac {25 \, x^{2} e^{x} \log \left (3\right )}{\log \left (2\right )} - \frac {25 i \, \pi x^{2} \log \left (x\right )}{\log \left (2\right )} - \frac {25 \, x^{2} \log \left (3\right ) \log \left (x\right )}{\log \left (2\right )} + \frac {125 \, x^{2}}{\log \left (2\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.50, size = 82, normalized size = 2.65 \begin {gather*} e^{\left (\frac {25 i \, \pi x^{3}}{\log \left (2\right )} + \frac {25 i \, \pi x^{2} e^{x}}{\log \left (2\right )} + \frac {25 \, x^{3} \log \left (3\right )}{\log \left (2\right )} + \frac {25 \, x^{2} e^{x} \log \left (3\right )}{\log \left (2\right )} - \frac {25 i \, \pi x^{2} \log \left (x\right )}{\log \left (2\right )} - \frac {25 \, x^{2} \log \left (3\right ) \log \left (x\right )}{\log \left (2\right )} + \frac {125 \, x^{2}}{\log \left (2\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.54, size = 78, normalized size = 2.52 \begin {gather*} \frac {{847288609443}^{\frac {x^2\,{\mathrm {e}}^x+x^3}{\ln \left (2\right )}}\,{\mathrm {e}}^{\frac {125\,x^2}{\ln \left (2\right )}}\,{\mathrm {e}}^{\frac {\Pi \,x^2\,{\mathrm {e}}^x\,25{}\mathrm {i}}{\ln \left (2\right )}}\,{\mathrm {e}}^{\frac {\Pi \,x^3\,25{}\mathrm {i}}{\ln \left (2\right )}}}{x^{\frac {25\,x^2\,\ln \left (3\right )+\Pi \,x^2\,25{}\mathrm {i}}{\ln \left (2\right )}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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