Optimal. Leaf size=24 \[ \frac {1}{x-e^{\frac {1}{30} x \left (3+\frac {-2+x}{\log (x)}\right )} x} \]
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Rubi [F] time = 10.06, 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 {-30 \log ^2(x)+e^{\frac {-2 x+x^2+3 x \log (x)}{30 \log (x)}} \left (2 x-x^2+\left (-2 x+2 x^2\right ) \log (x)+(30+3 x) \log ^2(x)\right )}{30 x^2 \log ^2(x)-60 e^{\frac {-2 x+x^2+3 x \log (x)}{30 \log (x)}} x^2 \log ^2(x)+30 e^{\frac {-2 x+x^2+3 x \log (x)}{15 \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 {2 x}{15 \log (x)}} \left (-30 \log ^2(x)+e^{\frac {-2 x+x^2+3 x \log (x)}{30 \log (x)}} \left (2 x-x^2+\left (-2 x+2 x^2\right ) \log (x)+(30+3 x) \log ^2(x)\right )\right )}{30 \left (e^{\frac {x}{15 \log (x)}}-e^{\frac {x (x+3 \log (x))}{30 \log (x)}}\right )^2 x^2 \log ^2(x)} \, dx\\ &=\frac {1}{30} \int \frac {e^{\frac {2 x}{15 \log (x)}} \left (-30 \log ^2(x)+e^{\frac {-2 x+x^2+3 x \log (x)}{30 \log (x)}} \left (2 x-x^2+\left (-2 x+2 x^2\right ) \log (x)+(30+3 x) \log ^2(x)\right )\right )}{\left (e^{\frac {x}{15 \log (x)}}-e^{\frac {x (x+3 \log (x))}{30 \log (x)}}\right )^2 x^2 \log ^2(x)} \, dx\\ &=\frac {1}{30} \int \left (-\frac {30 e^{\frac {2 x}{15 \log (x)}}}{\left (e^{\frac {x}{15 \log (x)}}-e^{\frac {x (x+3 \log (x))}{30 \log (x)}}\right )^2 x^2}+\frac {30 \exp \left (\frac {2 x}{15 \log (x)}+\frac {x (-2+x+3 \log (x))}{30 \log (x)}\right )}{\left (e^{\frac {x}{15 \log (x)}}-e^{\frac {x (x+3 \log (x))}{30 \log (x)}}\right )^2 x^2}+\frac {3 \exp \left (\frac {2 x}{15 \log (x)}+\frac {x (-2+x+3 \log (x))}{30 \log (x)}\right )}{\left (e^{\frac {x}{15 \log (x)}}-e^{\frac {x (x+3 \log (x))}{30 \log (x)}}\right )^2 x}-\frac {\exp \left (\frac {2 x}{15 \log (x)}+\frac {x (-2+x+3 \log (x))}{30 \log (x)}\right )}{\left (e^{\frac {x}{15 \log (x)}}-e^{\frac {x (x+3 \log (x))}{30 \log (x)}}\right )^2 \log ^2(x)}+\frac {2 \exp \left (\frac {2 x}{15 \log (x)}+\frac {x (-2+x+3 \log (x))}{30 \log (x)}\right )}{\left (e^{\frac {x}{15 \log (x)}}-e^{\frac {x (x+3 \log (x))}{30 \log (x)}}\right )^2 x \log ^2(x)}+\frac {2 \exp \left (\frac {2 x}{15 \log (x)}+\frac {x (-2+x+3 \log (x))}{30 \log (x)}\right )}{\left (e^{\frac {x}{15 \log (x)}}-e^{\frac {x (x+3 \log (x))}{30 \log (x)}}\right )^2 \log (x)}-\frac {2 \exp \left (\frac {2 x}{15 \log (x)}+\frac {x (-2+x+3 \log (x))}{30 \log (x)}\right )}{\left (e^{\frac {x}{15 \log (x)}}-e^{\frac {x (x+3 \log (x))}{30 \log (x)}}\right )^2 x \log (x)}\right ) \, dx\\ &=-\left (\frac {1}{30} \int \frac {\exp \left (\frac {2 x}{15 \log (x)}+\frac {x (-2+x+3 \log (x))}{30 \log (x)}\right )}{\left (e^{\frac {x}{15 \log (x)}}-e^{\frac {x (x+3 \log (x))}{30 \log (x)}}\right )^2 \log ^2(x)} \, dx\right )+\frac {1}{15} \int \frac {\exp \left (\frac {2 x}{15 \log (x)}+\frac {x (-2+x+3 \log (x))}{30 \log (x)}\right )}{\left (e^{\frac {x}{15 \log (x)}}-e^{\frac {x (x+3 \log (x))}{30 \log (x)}}\right )^2 x \log ^2(x)} \, dx+\frac {1}{15} \int \frac {\exp \left (\frac {2 x}{15 \log (x)}+\frac {x (-2+x+3 \log (x))}{30 \log (x)}\right )}{\left (e^{\frac {x}{15 \log (x)}}-e^{\frac {x (x+3 \log (x))}{30 \log (x)}}\right )^2 \log (x)} \, dx-\frac {1}{15} \int \frac {\exp \left (\frac {2 x}{15 \log (x)}+\frac {x (-2+x+3 \log (x))}{30 \log (x)}\right )}{\left (e^{\frac {x}{15 \log (x)}}-e^{\frac {x (x+3 \log (x))}{30 \log (x)}}\right )^2 x \log (x)} \, dx+\frac {1}{10} \int \frac {\exp \left (\frac {2 x}{15 \log (x)}+\frac {x (-2+x+3 \log (x))}{30 \log (x)}\right )}{\left (e^{\frac {x}{15 \log (x)}}-e^{\frac {x (x+3 \log (x))}{30 \log (x)}}\right )^2 x} \, dx-\int \frac {e^{\frac {2 x}{15 \log (x)}}}{\left (e^{\frac {x}{15 \log (x)}}-e^{\frac {x (x+3 \log (x))}{30 \log (x)}}\right )^2 x^2} \, dx+\int \frac {\exp \left (\frac {2 x}{15 \log (x)}+\frac {x (-2+x+3 \log (x))}{30 \log (x)}\right )}{\left (e^{\frac {x}{15 \log (x)}}-e^{\frac {x (x+3 \log (x))}{30 \log (x)}}\right )^2 x^2} \, dx\\ &=-\left (\frac {1}{30} \int \frac {e^{\frac {x (2+x+3 \log (x))}{30 \log (x)}}}{\left (e^{\frac {x}{15 \log (x)}}-e^{\frac {x (x+3 \log (x))}{30 \log (x)}}\right )^2 \log ^2(x)} \, dx\right )+\frac {1}{15} \int \frac {e^{\frac {x (2+x+3 \log (x))}{30 \log (x)}}}{\left (e^{\frac {x}{15 \log (x)}}-e^{\frac {x (x+3 \log (x))}{30 \log (x)}}\right )^2 x \log ^2(x)} \, dx+\frac {1}{15} \int \frac {e^{\frac {x (2+x+3 \log (x))}{30 \log (x)}}}{\left (e^{\frac {x}{15 \log (x)}}-e^{\frac {x (x+3 \log (x))}{30 \log (x)}}\right )^2 \log (x)} \, dx-\frac {1}{15} \int \frac {e^{\frac {x (2+x+3 \log (x))}{30 \log (x)}}}{\left (e^{\frac {x}{15 \log (x)}}-e^{\frac {x (x+3 \log (x))}{30 \log (x)}}\right )^2 x \log (x)} \, dx+\frac {1}{10} \int \frac {e^{\frac {x (2+x+3 \log (x))}{30 \log (x)}}}{\left (e^{\frac {x}{15 \log (x)}}-e^{\frac {x (x+3 \log (x))}{30 \log (x)}}\right )^2 x} \, dx-\int \frac {e^{\frac {2 x}{15 \log (x)}}}{\left (e^{\frac {x}{15 \log (x)}}-e^{\frac {x (x+3 \log (x))}{30 \log (x)}}\right )^2 x^2} \, dx+\int \frac {e^{\frac {x (2+x+3 \log (x))}{30 \log (x)}}}{\left (e^{\frac {x}{15 \log (x)}}-e^{\frac {x (x+3 \log (x))}{30 \log (x)}}\right )^2 x^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [F] time = 180.00, size = 0, normalized size = 0.00 \begin {gather*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.85, size = 29, normalized size = 1.21 \begin {gather*} -\frac {1}{x e^{\left (\frac {x^{2} + 3 \, x \log \relax (x) - 2 \, x}{30 \, \log \relax (x)}\right )} - x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 25, normalized size = 1.04
method | result | size |
risch | \(-\frac {1}{x \left ({\mathrm e}^{\frac {x \left (3 \ln \relax (x )+x -2\right )}{30 \ln \relax (x )}}-1\right )}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \frac {1}{30} \, \int \frac {{\left (3 \, {\left (x + 10\right )} \log \relax (x)^{2} - x^{2} + 2 \, {\left (x^{2} - x\right )} \log \relax (x) + 2 \, x\right )} e^{\left (\frac {x^{2} + 3 \, x \log \relax (x) - 2 \, x}{30 \, \log \relax (x)}\right )} - 30 \, \log \relax (x)^{2}}{x^{2} e^{\left (\frac {x^{2} + 3 \, x \log \relax (x) - 2 \, x}{15 \, \log \relax (x)}\right )} \log \relax (x)^{2} - 2 \, x^{2} e^{\left (\frac {x^{2} + 3 \, x \log \relax (x) - 2 \, x}{30 \, \log \relax (x)}\right )} \log \relax (x)^{2} + x^{2} \log \relax (x)^{2}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 6.16, size = 77, normalized size = 3.21 \begin {gather*} -\frac {x\,\left (3\,{\ln \relax (x)}^2-2\,\ln \relax (x)+2\right )+x^2\,\left (2\,\ln \relax (x)-1\right )}{x^2\,\left ({\mathrm {e}}^{\frac {x}{10}-\frac {x}{15\,\ln \relax (x)}+\frac {x^2}{30\,\ln \relax (x)}}-1\right )\,\left (3\,{\ln \relax (x)}^2-2\,\ln \relax (x)-x+2\,x\,\ln \relax (x)+2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.42, size = 26, normalized size = 1.08 \begin {gather*} - \frac {1}{x e^{\frac {\frac {x^{2}}{30} + \frac {x \log {\relax (x )}}{10} - \frac {x}{15}}{\log {\relax (x )}}} - x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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