Optimal. Leaf size=27 \[ \frac {e^{4-x+x^2} x^3}{9 (-5+x) \log (\log (x))} \]
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Rubi [F] time = 2.99, 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^{4-x+x^2} \left (5 x^2-x^3+\left (-15 x^2+7 x^3-11 x^4+2 x^5\right ) \log (x) \log (\log (x))\right )}{\left (225-90 x+9 x^2\right ) \log (x) \log ^2(\log (x))} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{4-x+x^2} \left (5 x^2-x^3+\left (-15 x^2+7 x^3-11 x^4+2 x^5\right ) \log (x) \log (\log (x))\right )}{9 (-5+x)^2 \log (x) \log ^2(\log (x))} \, dx\\ &=\frac {1}{9} \int \frac {e^{4-x+x^2} \left (5 x^2-x^3+\left (-15 x^2+7 x^3-11 x^4+2 x^5\right ) \log (x) \log (\log (x))\right )}{(-5+x)^2 \log (x) \log ^2(\log (x))} \, dx\\ &=\frac {1}{9} \int \left (-\frac {e^{4-x+x^2} x^2}{(-5+x) \log (x) \log ^2(\log (x))}+\frac {e^{4-x+x^2} x^2 \left (-15+7 x-11 x^2+2 x^3\right )}{(-5+x)^2 \log (\log (x))}\right ) \, dx\\ &=-\left (\frac {1}{9} \int \frac {e^{4-x+x^2} x^2}{(-5+x) \log (x) \log ^2(\log (x))} \, dx\right )+\frac {1}{9} \int \frac {e^{4-x+x^2} x^2 \left (-15+7 x-11 x^2+2 x^3\right )}{(-5+x)^2 \log (\log (x))} \, dx\\ &=-\left (\frac {1}{9} \int \left (\frac {5 e^{4-x+x^2}}{\log (x) \log ^2(\log (x))}+\frac {25 e^{4-x+x^2}}{(-5+x) \log (x) \log ^2(\log (x))}+\frac {e^{4-x+x^2} x}{\log (x) \log ^2(\log (x))}\right ) \, dx\right )+\frac {1}{9} \int \left (\frac {230 e^{4-x+x^2}}{\log (\log (x))}-\frac {125 e^{4-x+x^2}}{(-5+x)^2 \log (\log (x))}+\frac {1125 e^{4-x+x^2}}{(-5+x) \log (\log (x))}+\frac {47 e^{4-x+x^2} x}{\log (\log (x))}+\frac {9 e^{4-x+x^2} x^2}{\log (\log (x))}+\frac {2 e^{4-x+x^2} x^3}{\log (\log (x))}\right ) \, dx\\ &=-\left (\frac {1}{9} \int \frac {e^{4-x+x^2} x}{\log (x) \log ^2(\log (x))} \, dx\right )+\frac {2}{9} \int \frac {e^{4-x+x^2} x^3}{\log (\log (x))} \, dx-\frac {5}{9} \int \frac {e^{4-x+x^2}}{\log (x) \log ^2(\log (x))} \, dx-\frac {25}{9} \int \frac {e^{4-x+x^2}}{(-5+x) \log (x) \log ^2(\log (x))} \, dx+\frac {47}{9} \int \frac {e^{4-x+x^2} x}{\log (\log (x))} \, dx-\frac {125}{9} \int \frac {e^{4-x+x^2}}{(-5+x)^2 \log (\log (x))} \, dx+\frac {230}{9} \int \frac {e^{4-x+x^2}}{\log (\log (x))} \, dx+125 \int \frac {e^{4-x+x^2}}{(-5+x) \log (\log (x))} \, dx+\int \frac {e^{4-x+x^2} x^2}{\log (\log (x))} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.49, size = 27, normalized size = 1.00 \begin {gather*} \frac {e^{4-x+x^2} x^3}{9 (-5+x) \log (\log (x))} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.71, size = 25, normalized size = 0.93 \begin {gather*} \frac {x^{3} e^{\left (x^{2} - x - \log \left (\log \left (\log \relax (x)\right )\right ) + 4\right )}}{9 \, {\left (x - 5\right )}} \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*} \mathit {undef} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.18, size = 25, normalized size = 0.93
method | result | size |
risch | \(\frac {x^{3} {\mathrm e}^{x^{2}-x +4}}{9 \left (x -5\right ) \ln \left (\ln \relax (x )\right )}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 24, normalized size = 0.89 \begin {gather*} \frac {x^{3} e^{\left (x^{2} - x + 4\right )}}{9 \, {\left (x - 5\right )} \log \left (\log \relax (x)\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.79, size = 29, normalized size = 1.07 \begin {gather*} -\frac {x^3\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^4}{9\,\left (5\,\ln \left (\ln \relax (x)\right )-x\,\ln \left (\ln \relax (x)\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.45, size = 26, normalized size = 0.96 \begin {gather*} \frac {x^{3} e^{x^{2} - x + 4}}{9 x \log {\left (\log {\relax (x )} \right )} - 45 \log {\left (\log {\relax (x )} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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