Integrand size = 62, antiderivative size = 26 \[ \int \frac {e^{-1-3 x} \log ^2\left (-x+x^2\right ) \left ((-9+18 x) \log (x)+\left (-3+3 x+\left (9-9 x^2\right ) \log (x)\right ) \log \left (-x+x^2\right )\right )}{-x^4+x^5} \, dx=\frac {3 e^{-1+3 \left (-x+\log \left (\log \left (-x+x^2\right )\right )\right )} \log (x)}{x^3} \]
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\[ \int \frac {e^{-1-3 x} \log ^2\left (-x+x^2\right ) \left ((-9+18 x) \log (x)+\left (-3+3 x+\left (9-9 x^2\right ) \log (x)\right ) \log \left (-x+x^2\right )\right )}{-x^4+x^5} \, dx=\int \frac {e^{-1-3 x} \log ^2\left (-x+x^2\right ) \left ((-9+18 x) \log (x)+\left (-3+3 x+\left (9-9 x^2\right ) \log (x)\right ) \log \left (-x+x^2\right )\right )}{-x^4+x^5} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {e^{-1-3 x} \log ^2\left (-x+x^2\right ) \left ((-9+18 x) \log (x)+\left (-3+3 x+\left (9-9 x^2\right ) \log (x)\right ) \log \left (-x+x^2\right )\right )}{(-1+x) x^4} \, dx \\ & = \int \frac {e^{-1-3 x} \log ^2((-1+x) x) \left (-((-9+18 x) \log (x))-\left (-3+3 x+\left (9-9 x^2\right ) \log (x)\right ) \log \left (-x+x^2\right )\right )}{(1-x) x^4} \, dx \\ & = \int \left (\frac {9 e^{-1-3 x} (-1+2 x) \log (x) \log ^2((-1+x) x)}{(-1+x) x^4}-\frac {3 e^{-1-3 x} (-1+3 \log (x)+3 x \log (x)) \log ^3((-1+x) x)}{x^4}\right ) \, dx \\ & = -\left (3 \int \frac {e^{-1-3 x} (-1+3 \log (x)+3 x \log (x)) \log ^3((-1+x) x)}{x^4} \, dx\right )+9 \int \frac {e^{-1-3 x} (-1+2 x) \log (x) \log ^2((-1+x) x)}{(-1+x) x^4} \, dx \\ & = -\left (3 \int \left (-\frac {e^{-1-3 x} \log ^3((-1+x) x)}{x^4}+\frac {3 e^{-1-3 x} \log (x) \log ^3((-1+x) x)}{x^4}+\frac {3 e^{-1-3 x} \log (x) \log ^3((-1+x) x)}{x^3}\right ) \, dx\right )+9 \int \left (\frac {e^{-1-3 x} \log (x) \log ^2((-1+x) x)}{-1+x}+\frac {e^{-1-3 x} \log (x) \log ^2((-1+x) x)}{x^4}-\frac {e^{-1-3 x} \log (x) \log ^2((-1+x) x)}{x^3}-\frac {e^{-1-3 x} \log (x) \log ^2((-1+x) x)}{x^2}-\frac {e^{-1-3 x} \log (x) \log ^2((-1+x) x)}{x}\right ) \, dx \\ & = 3 \int \frac {e^{-1-3 x} \log ^3((-1+x) x)}{x^4} \, dx+9 \int \frac {e^{-1-3 x} \log (x) \log ^2((-1+x) x)}{-1+x} \, dx+9 \int \frac {e^{-1-3 x} \log (x) \log ^2((-1+x) x)}{x^4} \, dx-9 \int \frac {e^{-1-3 x} \log (x) \log ^2((-1+x) x)}{x^3} \, dx-9 \int \frac {e^{-1-3 x} \log (x) \log ^2((-1+x) x)}{x^2} \, dx-9 \int \frac {e^{-1-3 x} \log (x) \log ^2((-1+x) x)}{x} \, dx-9 \int \frac {e^{-1-3 x} \log (x) \log ^3((-1+x) x)}{x^4} \, dx-9 \int \frac {e^{-1-3 x} \log (x) \log ^3((-1+x) x)}{x^3} \, dx \\ \end{align*}
Time = 0.68 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.85 \[ \int \frac {e^{-1-3 x} \log ^2\left (-x+x^2\right ) \left ((-9+18 x) \log (x)+\left (-3+3 x+\left (9-9 x^2\right ) \log (x)\right ) \log \left (-x+x^2\right )\right )}{-x^4+x^5} \, dx=\frac {3 e^{-1-3 x} \log (x) \log ^3((-1+x) x)}{x^3} \]
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Time = 7.02 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.08
method | result | size |
parallelrisch | \(\frac {3 \ln \left (x \right ) {\mathrm e}^{-1} {\mathrm e}^{3 \ln \left (\ln \left (x^{2}-x \right )\right )-3 x}}{x^{3}}\) | \(28\) |
risch | \(\text {Expression too large to display}\) | \(1414\) |
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Time = 0.26 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.92 \[ \int \frac {e^{-1-3 x} \log ^2\left (-x+x^2\right ) \left ((-9+18 x) \log (x)+\left (-3+3 x+\left (9-9 x^2\right ) \log (x)\right ) \log \left (-x+x^2\right )\right )}{-x^4+x^5} \, dx=\frac {3 \, e^{\left (-3 \, x + 3 \, \log \left (\log \left (x^{2} - x\right )\right ) - 1\right )} \log \left (x\right )}{x^{3}} \]
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Time = 0.16 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.92 \[ \int \frac {e^{-1-3 x} \log ^2\left (-x+x^2\right ) \left ((-9+18 x) \log (x)+\left (-3+3 x+\left (9-9 x^2\right ) \log (x)\right ) \log \left (-x+x^2\right )\right )}{-x^4+x^5} \, dx=\frac {3 e^{- 3 x} \log {\left (x \right )} \log {\left (x^{2} - x \right )}^{3}}{e x^{3}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 60 vs. \(2 (24) = 48\).
Time = 0.27 (sec) , antiderivative size = 60, normalized size of antiderivative = 2.31 \[ \int \frac {e^{-1-3 x} \log ^2\left (-x+x^2\right ) \left ((-9+18 x) \log (x)+\left (-3+3 x+\left (9-9 x^2\right ) \log (x)\right ) \log \left (-x+x^2\right )\right )}{-x^4+x^5} \, dx=\frac {3 \, {\left (e^{\left (-3 \, x\right )} \log \left (x - 1\right )^{3} \log \left (x\right ) + 3 \, e^{\left (-3 \, x\right )} \log \left (x - 1\right )^{2} \log \left (x\right )^{2} + 3 \, e^{\left (-3 \, x\right )} \log \left (x - 1\right ) \log \left (x\right )^{3} + e^{\left (-3 \, x\right )} \log \left (x\right )^{4}\right )} e^{\left (-1\right )}}{x^{3}} \]
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\[ \int \frac {e^{-1-3 x} \log ^2\left (-x+x^2\right ) \left ((-9+18 x) \log (x)+\left (-3+3 x+\left (9-9 x^2\right ) \log (x)\right ) \log \left (-x+x^2\right )\right )}{-x^4+x^5} \, dx=\int { -\frac {3 \, {\left ({\left (3 \, {\left (x^{2} - 1\right )} \log \left (x\right ) - x + 1\right )} \log \left (x^{2} - x\right ) - 3 \, {\left (2 \, x - 1\right )} \log \left (x\right )\right )} e^{\left (-3 \, x + 3 \, \log \left (\log \left (x^{2} - x\right )\right ) - 1\right )}}{{\left (x^{5} - x^{4}\right )} \log \left (x^{2} - x\right )} \,d x } \]
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Timed out. \[ \int \frac {e^{-1-3 x} \log ^2\left (-x+x^2\right ) \left ((-9+18 x) \log (x)+\left (-3+3 x+\left (9-9 x^2\right ) \log (x)\right ) \log \left (-x+x^2\right )\right )}{-x^4+x^5} \, dx=\int -\frac {{\mathrm {e}}^{-1}\,{\mathrm {e}}^{3\,\ln \left (\ln \left (x^2-x\right )\right )-3\,x}\,\left (\ln \left (x\right )\,\left (18\,x-9\right )-\ln \left (x^2-x\right )\,\left (\ln \left (x\right )\,\left (9\,x^2-9\right )-3\,x+3\right )\right )}{\ln \left (x^2-x\right )\,\left (x^4-x^5\right )} \,d x \]
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