Optimal. Leaf size=27 \[ e^{\frac {9}{x \left (\frac {x}{2}+\frac {x}{\log (x)}\right ) \log (x)}} x \]
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Rubi [F] time = 1.00, 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^{\frac {18}{2 x^2+x^2 \log (x)}} \left (-90+4 x^2+\left (-36+4 x^2\right ) \log (x)+x^2 \log ^2(x)\right )}{4 x^2+4 x^2 \log (x)+x^2 \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 \frac {e^{\frac {18}{x^2 (2+\log (x))}} \left (-90+4 x^2+4 \left (-9+x^2\right ) \log (x)+x^2 \log ^2(x)\right )}{x^2 (2+\log (x))^2} \, dx\\ &=\int \left (e^{\frac {18}{x^2 (2+\log (x))}}-\frac {18 e^{\frac {18}{x^2 (2+\log (x))}}}{x^2 (2+\log (x))^2}-\frac {36 e^{\frac {18}{x^2 (2+\log (x))}}}{x^2 (2+\log (x))}\right ) \, dx\\ &=-\left (18 \int \frac {e^{\frac {18}{x^2 (2+\log (x))}}}{x^2 (2+\log (x))^2} \, dx\right )-36 \int \frac {e^{\frac {18}{x^2 (2+\log (x))}}}{x^2 (2+\log (x))} \, dx+\int e^{\frac {18}{x^2 (2+\log (x))}} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.18, size = 15, normalized size = 0.56 \begin {gather*} e^{\frac {18}{x^2 (2+\log (x))}} x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 19, normalized size = 0.70 \begin {gather*} x e^{\left (\frac {18}{x^{2} \log \relax (x) + 2 \, x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.42, size = 19, normalized size = 0.70 \begin {gather*} x e^{\left (\frac {18}{x^{2} \log \relax (x) + 2 \, x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 15, normalized size = 0.56
method | result | size |
risch | \(x \,{\mathrm e}^{\frac {18}{x^{2} \left (\ln \relax (x )+2\right )}}\) | \(15\) |
norman | \(\frac {x^{2} \ln \relax (x ) {\mathrm e}^{\frac {18}{x^{2} \ln \relax (x )+2 x^{2}}}+2 x^{2} {\mathrm e}^{\frac {18}{x^{2} \ln \relax (x )+2 x^{2}}}}{\left (\ln \relax (x )+2\right ) x}\) | \(57\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: RuntimeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.37, size = 14, normalized size = 0.52 \begin {gather*} x\,{\mathrm {e}}^{\frac {18}{x^2\,\left (\ln \relax (x)+2\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 3.96, size = 15, normalized size = 0.56 \begin {gather*} x e^{\frac {18}{x^{2} \log {\relax (x )} + 2 x^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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