Optimal. Leaf size=21 \[ e^{x^{-8-2 x+2 \log \left (3 e^x \log ^2(x)\right )}} \]
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Rubi [F]
time = 2.16, 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 \exp \left (\exp \left (2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2+2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) \left (-4 x-2 x^2+2 x \log \left (3 e^x \log ^2(x)\right )\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int 2 \exp \left (\exp \left (2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2+2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x \left (-2-x+\log \left (3 e^x \log ^2(x)\right )\right ) \, dx\\ &=2 \int \exp \left (\exp \left (2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2+2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x \left (-2-x+\log \left (3 e^x \log ^2(x)\right )\right ) \, dx\\ &=2 \int \left (-\exp \left (\exp \left (2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2+2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x (2+x)+\exp \left (\exp \left (2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2+2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x \log \left (3 e^x \log ^2(x)\right )\right ) \, dx\\ &=-\left (2 \int \exp \left (\exp \left (2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2+2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x (2+x) \, dx\right )+2 \int \exp \left (\exp \left (2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2+2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x \log \left (3 e^x \log ^2(x)\right ) \, dx\\ &=-\left (2 \int \left (2 \exp \left (\exp \left (2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2+2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x+\exp \left (\exp \left (2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2+2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2\right ) \, dx\right )+2 \int \exp \left (\exp \left (2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2+2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x \log \left (3 e^x \log ^2(x)\right ) \, dx\\ &=-\left (2 \int \exp \left (\exp \left (2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2+2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2 \, dx\right )+2 \int \exp \left (\exp \left (2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2+2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x \log \left (3 e^x \log ^2(x)\right ) \, dx-4 \int \exp \left (\exp \left (2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2+2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x \, dx\\ &=-\left (2 \int \exp \left (x^{-8-2 x+2 \log \left (3 e^x \log ^2(x)\right )}+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^{-8-2 x} \, dx\right )+2 \int \exp \left (\exp \left (2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2+2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x \log \left (3 e^x \log ^2(x)\right ) \, dx-4 \int \exp \left (\exp \left (2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x^2+2 (-5-x) \log (x)+2 \log (x) \log \left (3 e^x \log ^2(x)\right )\right ) x \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.60, size = 21, normalized size = 1.00 \begin {gather*} e^{x^{-8-2 x+2 \log \left (3 e^x \log ^2(x)\right )}} \end {gather*}
Antiderivative was successfully verified.
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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order
3.
time = 0.44, size = 104, normalized size = 4.95
method | result | size |
risch | \({\mathrm e}^{x^{2} x^{-i \mathrm {csgn}\left (i \ln \left (x \right )^{2}\right ) \pi +2 i \pi \,\mathrm {csgn}\left (i \ln \left (x \right )\right )-i \pi \,\mathrm {csgn}\left (i \ln \left (x \right )^{2}\right ) \mathrm {csgn}\left (i {\mathrm e}^{x} \ln \left (x \right )^{2}\right ) \mathrm {csgn}\left (i {\mathrm e}^{x}\right )-i \mathrm {csgn}\left (i {\mathrm e}^{x} \ln \left (x \right )^{2}\right ) \pi +4 \ln \left (\ln \left (x \right )\right )+2 \ln \left (3 \,{\mathrm e}^{x}\right )+i \pi \,\mathrm {csgn}\left (i {\mathrm e}^{x}\right )} x^{-2 x -10}}\) | \(104\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.73, size = 20, normalized size = 0.95 \begin {gather*} e^{\left (\frac {e^{\left (2 \, \log \left (3\right ) \log \left (x\right ) + 4 \, \log \left (x\right ) \log \left (\log \left (x\right )\right )\right )}}{x^{8}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 27, normalized size = 1.29 \begin {gather*} e^{\left (x^{2} e^{\left (-2 \, {\left (x + 5\right )} \log \left (x\right ) + 2 \, \log \left (3 \, e^{x} \log \left (x\right )^{2}\right ) \log \left (x\right )\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 [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.
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Mupad [B]
time = 1.23, size = 20, normalized size = 0.95 \begin {gather*} {\mathrm {e}}^{\frac {x^{2\,\ln \left (3\right )}\,x^{2\,\ln \left ({\ln \left (x\right )}^2\right )}}{x^8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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