Integrand size = 352, antiderivative size = 35 \[ \int \frac {-3 e^3 x^2+3 x^3+e^{-2-2 x} \left (-18 e^3+18 x\right )+e^{-1-x} \left (-15 e^3 x+12 x^2-3 x^3\right )+\left (e^{-2-2 x} \left (-18+18 e^3\right )-3 x^2+3 e^3 x^2+e^{-1-x} \left (-12 x+15 e^3 x+3 x^2\right )\right ) \log (x)+\left (18 e^{-2-2 x}+15 e^{-1-x} x+3 x^2+\left (-18 e^{-2-2 x}-15 e^{-1-x} x-3 x^2\right ) \log (x)\right ) \log \left (\frac {3 e^{-1-x} x+x^2}{2 e^{-1-x}+x}\right )}{6 e^{4-2 x} x^2+5 e^{5-x} x^3+e^6 x^4+\left (-12 e^{1-2 x} x^2-10 e^{2-x} x^3-2 e^3 x^4\right ) \log \left (\frac {3 e^{-1-x} x+x^2}{2 e^{-1-x}+x}\right )+\left (6 e^{-2-2 x} x^2+5 e^{-1-x} x^3+x^4\right ) \log ^2\left (\frac {3 e^{-1-x} x+x^2}{2 e^{-1-x}+x}\right )} \, dx=\frac {3 (-x+\log (x))}{x \left (-e^3+\log \left (x+\frac {x}{2+e^{1+x} x}\right )\right )} \]
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\[ \int \frac {-3 e^3 x^2+3 x^3+e^{-2-2 x} \left (-18 e^3+18 x\right )+e^{-1-x} \left (-15 e^3 x+12 x^2-3 x^3\right )+\left (e^{-2-2 x} \left (-18+18 e^3\right )-3 x^2+3 e^3 x^2+e^{-1-x} \left (-12 x+15 e^3 x+3 x^2\right )\right ) \log (x)+\left (18 e^{-2-2 x}+15 e^{-1-x} x+3 x^2+\left (-18 e^{-2-2 x}-15 e^{-1-x} x-3 x^2\right ) \log (x)\right ) \log \left (\frac {3 e^{-1-x} x+x^2}{2 e^{-1-x}+x}\right )}{6 e^{4-2 x} x^2+5 e^{5-x} x^3+e^6 x^4+\left (-12 e^{1-2 x} x^2-10 e^{2-x} x^3-2 e^3 x^4\right ) \log \left (\frac {3 e^{-1-x} x+x^2}{2 e^{-1-x}+x}\right )+\left (6 e^{-2-2 x} x^2+5 e^{-1-x} x^3+x^4\right ) \log ^2\left (\frac {3 e^{-1-x} x+x^2}{2 e^{-1-x}+x}\right )} \, dx=\int \frac {-3 e^3 x^2+3 x^3+e^{-2-2 x} \left (-18 e^3+18 x\right )+e^{-1-x} \left (-15 e^3 x+12 x^2-3 x^3\right )+\left (e^{-2-2 x} \left (-18+18 e^3\right )-3 x^2+3 e^3 x^2+e^{-1-x} \left (-12 x+15 e^3 x+3 x^2\right )\right ) \log (x)+\left (18 e^{-2-2 x}+15 e^{-1-x} x+3 x^2+\left (-18 e^{-2-2 x}-15 e^{-1-x} x-3 x^2\right ) \log (x)\right ) \log \left (\frac {3 e^{-1-x} x+x^2}{2 e^{-1-x}+x}\right )}{6 e^{4-2 x} x^2+5 e^{5-x} x^3+e^6 x^4+\left (-12 e^{1-2 x} x^2-10 e^{2-x} x^3-2 e^3 x^4\right ) \log \left (\frac {3 e^{-1-x} x+x^2}{2 e^{-1-x}+x}\right )+\left (6 e^{-2-2 x} x^2+5 e^{-1-x} x^3+x^4\right ) \log ^2\left (\frac {3 e^{-1-x} x+x^2}{2 e^{-1-x}+x}\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {3 \left (-6 e^3+6 x-5 e^{4+x} x+4 e^{1+x} x^2-e^{5+2 x} x^2-e^{1+x} x^3+e^{2+2 x} x^3+\left (6+5 e^{1+x} x+e^{2+2 x} x^2\right ) \log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )+\log (x) \left (-6+6 e^3+5 e^{4+x} x+e^{1+x} (-4+x) x-e^{2+2 x} x^2+e^{5+2 x} x^2-\left (6+5 e^{1+x} x+e^{2+2 x} x^2\right ) \log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )\right )}{x^2 \left (6+5 e^{1+x} x+e^{2+2 x} x^2\right ) \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2} \, dx \\ & = 3 \int \frac {-6 e^3+6 x-5 e^{4+x} x+4 e^{1+x} x^2-e^{5+2 x} x^2-e^{1+x} x^3+e^{2+2 x} x^3+\left (6+5 e^{1+x} x+e^{2+2 x} x^2\right ) \log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )+\log (x) \left (-6+6 e^3+5 e^{4+x} x+e^{1+x} (-4+x) x-e^{2+2 x} x^2+e^{5+2 x} x^2-\left (6+5 e^{1+x} x+e^{2+2 x} x^2\right ) \log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )}{x^2 \left (6+5 e^{1+x} x+e^{2+2 x} x^2\right ) \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2} \, dx \\ & = 3 \int \left (\frac {2 (1+x) (x-\log (x))}{x^2 \left (2+e^{1+x} x\right ) \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2}-\frac {3 (1+x) (x-\log (x))}{x^2 \left (3+e^{1+x} x\right ) \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2}+\frac {-e^3+x-\left (1-e^3\right ) \log (x)+\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )-\log (x) \log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )}{x^2 \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2}\right ) \, dx \\ & = 3 \int \frac {-e^3+x-\left (1-e^3\right ) \log (x)+\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )-\log (x) \log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )}{x^2 \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2} \, dx+6 \int \frac {(1+x) (x-\log (x))}{x^2 \left (2+e^{1+x} x\right ) \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2} \, dx-9 \int \frac {(1+x) (x-\log (x))}{x^2 \left (3+e^{1+x} x\right ) \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2} \, dx \\ & = 3 \int \left (\frac {x-\log (x)}{x^2 \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2}+\frac {-1+\log (x)}{x^2 \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )}\right ) \, dx+6 \int \left (\frac {x-\log (x)}{x^2 \left (2+e^{1+x} x\right ) \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2}+\frac {x-\log (x)}{x \left (2+e^{1+x} x\right ) \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2}\right ) \, dx-9 \int \left (\frac {x-\log (x)}{x^2 \left (3+e^{1+x} x\right ) \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2}+\frac {x-\log (x)}{x \left (3+e^{1+x} x\right ) \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2}\right ) \, dx \\ & = 3 \int \frac {x-\log (x)}{x^2 \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2} \, dx+3 \int \frac {-1+\log (x)}{x^2 \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )} \, dx+6 \int \frac {x-\log (x)}{x^2 \left (2+e^{1+x} x\right ) \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2} \, dx+6 \int \frac {x-\log (x)}{x \left (2+e^{1+x} x\right ) \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2} \, dx-9 \int \frac {x-\log (x)}{x^2 \left (3+e^{1+x} x\right ) \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2} \, dx-9 \int \frac {x-\log (x)}{x \left (3+e^{1+x} x\right ) \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2} \, dx \\ & = 3 \int \left (\frac {1}{x \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2}-\frac {\log (x)}{x^2 \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2}\right ) \, dx+3 \int \left (-\frac {1}{x^2 \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )}+\frac {\log (x)}{x^2 \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )}\right ) \, dx+6 \int \left (\frac {1}{x \left (2+e^{1+x} x\right ) \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2}-\frac {\log (x)}{x^2 \left (2+e^{1+x} x\right ) \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2}\right ) \, dx+6 \int \left (\frac {1}{\left (2+e^{1+x} x\right ) \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2}-\frac {\log (x)}{x \left (2+e^{1+x} x\right ) \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2}\right ) \, dx-9 \int \left (\frac {1}{x \left (3+e^{1+x} x\right ) \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2}-\frac {\log (x)}{x^2 \left (3+e^{1+x} x\right ) \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2}\right ) \, dx-9 \int \left (\frac {1}{\left (3+e^{1+x} x\right ) \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2}-\frac {\log (x)}{x \left (3+e^{1+x} x\right ) \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2}\right ) \, dx \\ & = 3 \int \frac {1}{x \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2} \, dx-3 \int \frac {\log (x)}{x^2 \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2} \, dx-3 \int \frac {1}{x^2 \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )} \, dx+3 \int \frac {\log (x)}{x^2 \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )} \, dx+6 \int \frac {1}{\left (2+e^{1+x} x\right ) \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2} \, dx+6 \int \frac {1}{x \left (2+e^{1+x} x\right ) \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2} \, dx-6 \int \frac {\log (x)}{x^2 \left (2+e^{1+x} x\right ) \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2} \, dx-6 \int \frac {\log (x)}{x \left (2+e^{1+x} x\right ) \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2} \, dx-9 \int \frac {1}{\left (3+e^{1+x} x\right ) \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2} \, dx-9 \int \frac {1}{x \left (3+e^{1+x} x\right ) \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2} \, dx+9 \int \frac {\log (x)}{x^2 \left (3+e^{1+x} x\right ) \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2} \, dx+9 \int \frac {\log (x)}{x \left (3+e^{1+x} x\right ) \left (e^3-\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )^2} \, dx \\ \end{align*}
Time = 0.32 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.20 \[ \int \frac {-3 e^3 x^2+3 x^3+e^{-2-2 x} \left (-18 e^3+18 x\right )+e^{-1-x} \left (-15 e^3 x+12 x^2-3 x^3\right )+\left (e^{-2-2 x} \left (-18+18 e^3\right )-3 x^2+3 e^3 x^2+e^{-1-x} \left (-12 x+15 e^3 x+3 x^2\right )\right ) \log (x)+\left (18 e^{-2-2 x}+15 e^{-1-x} x+3 x^2+\left (-18 e^{-2-2 x}-15 e^{-1-x} x-3 x^2\right ) \log (x)\right ) \log \left (\frac {3 e^{-1-x} x+x^2}{2 e^{-1-x}+x}\right )}{6 e^{4-2 x} x^2+5 e^{5-x} x^3+e^6 x^4+\left (-12 e^{1-2 x} x^2-10 e^{2-x} x^3-2 e^3 x^4\right ) \log \left (\frac {3 e^{-1-x} x+x^2}{2 e^{-1-x}+x}\right )+\left (6 e^{-2-2 x} x^2+5 e^{-1-x} x^3+x^4\right ) \log ^2\left (\frac {3 e^{-1-x} x+x^2}{2 e^{-1-x}+x}\right )} \, dx=\frac {3 (-x+\log (x))}{x \left (-e^3+\log \left (\frac {x \left (3+e^{1+x} x\right )}{2+e^{1+x} x}\right )\right )} \]
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Time = 46.30 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.31
method | result | size |
parallelrisch | \(-\frac {3 \ln \left (x \right )-3 x}{x \left ({\mathrm e}^{3}-\ln \left (\frac {x \left (3 \,{\mathrm e}^{-1-x}+x \right )}{2 \,{\mathrm e}^{-1-x}+x}\right )\right )}\) | \(46\) |
risch | \(-\frac {6 \left (x -\ln \left (x \right )\right )}{x \left (-i \pi \,\operatorname {csgn}\left (\frac {i}{2 \,{\mathrm e}^{-1-x}+x}\right ) \operatorname {csgn}\left (i \left (3 \,{\mathrm e}^{-1-x}+x \right )\right ) \operatorname {csgn}\left (\frac {i \left (3 \,{\mathrm e}^{-1-x}+x \right )}{2 \,{\mathrm e}^{-1-x}+x}\right )+i \pi \,\operatorname {csgn}\left (\frac {i}{2 \,{\mathrm e}^{-1-x}+x}\right ) {\operatorname {csgn}\left (\frac {i \left (3 \,{\mathrm e}^{-1-x}+x \right )}{2 \,{\mathrm e}^{-1-x}+x}\right )}^{2}+i \pi \,\operatorname {csgn}\left (i \left (3 \,{\mathrm e}^{-1-x}+x \right )\right ) {\operatorname {csgn}\left (\frac {i \left (3 \,{\mathrm e}^{-1-x}+x \right )}{2 \,{\mathrm e}^{-1-x}+x}\right )}^{2}-i \pi {\operatorname {csgn}\left (\frac {i \left (3 \,{\mathrm e}^{-1-x}+x \right )}{2 \,{\mathrm e}^{-1-x}+x}\right )}^{3}+i \pi \,\operatorname {csgn}\left (\frac {i \left (3 \,{\mathrm e}^{-1-x}+x \right )}{2 \,{\mathrm e}^{-1-x}+x}\right ) {\operatorname {csgn}\left (\frac {i x \left (3 \,{\mathrm e}^{-1-x}+x \right )}{2 \,{\mathrm e}^{-1-x}+x}\right )}^{2}-i \pi \,\operatorname {csgn}\left (\frac {i \left (3 \,{\mathrm e}^{-1-x}+x \right )}{2 \,{\mathrm e}^{-1-x}+x}\right ) \operatorname {csgn}\left (\frac {i x \left (3 \,{\mathrm e}^{-1-x}+x \right )}{2 \,{\mathrm e}^{-1-x}+x}\right ) \operatorname {csgn}\left (i x \right )-i \pi {\operatorname {csgn}\left (\frac {i x \left (3 \,{\mathrm e}^{-1-x}+x \right )}{2 \,{\mathrm e}^{-1-x}+x}\right )}^{3}+i \pi {\operatorname {csgn}\left (\frac {i x \left (3 \,{\mathrm e}^{-1-x}+x \right )}{2 \,{\mathrm e}^{-1-x}+x}\right )}^{2} \operatorname {csgn}\left (i x \right )-2 \,{\mathrm e}^{3}+2 \ln \left (x \right )-2 \ln \left (2 \,{\mathrm e}^{-1-x}+x \right )+2 \ln \left (3 \,{\mathrm e}^{-1-x}+x \right )\right )}\) | \(427\) |
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Time = 0.27 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.46 \[ \int \frac {-3 e^3 x^2+3 x^3+e^{-2-2 x} \left (-18 e^3+18 x\right )+e^{-1-x} \left (-15 e^3 x+12 x^2-3 x^3\right )+\left (e^{-2-2 x} \left (-18+18 e^3\right )-3 x^2+3 e^3 x^2+e^{-1-x} \left (-12 x+15 e^3 x+3 x^2\right )\right ) \log (x)+\left (18 e^{-2-2 x}+15 e^{-1-x} x+3 x^2+\left (-18 e^{-2-2 x}-15 e^{-1-x} x-3 x^2\right ) \log (x)\right ) \log \left (\frac {3 e^{-1-x} x+x^2}{2 e^{-1-x}+x}\right )}{6 e^{4-2 x} x^2+5 e^{5-x} x^3+e^6 x^4+\left (-12 e^{1-2 x} x^2-10 e^{2-x} x^3-2 e^3 x^4\right ) \log \left (\frac {3 e^{-1-x} x+x^2}{2 e^{-1-x}+x}\right )+\left (6 e^{-2-2 x} x^2+5 e^{-1-x} x^3+x^4\right ) \log ^2\left (\frac {3 e^{-1-x} x+x^2}{2 e^{-1-x}+x}\right )} \, dx=\frac {3 \, {\left (x - \log \left (x\right )\right )}}{x e^{3} - x \log \left (\frac {x^{2} e^{6} + 3 \, x e^{\left (-x + 5\right )}}{x e^{6} + 2 \, e^{\left (-x + 5\right )}}\right )} \]
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Time = 0.42 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.11 \[ \int \frac {-3 e^3 x^2+3 x^3+e^{-2-2 x} \left (-18 e^3+18 x\right )+e^{-1-x} \left (-15 e^3 x+12 x^2-3 x^3\right )+\left (e^{-2-2 x} \left (-18+18 e^3\right )-3 x^2+3 e^3 x^2+e^{-1-x} \left (-12 x+15 e^3 x+3 x^2\right )\right ) \log (x)+\left (18 e^{-2-2 x}+15 e^{-1-x} x+3 x^2+\left (-18 e^{-2-2 x}-15 e^{-1-x} x-3 x^2\right ) \log (x)\right ) \log \left (\frac {3 e^{-1-x} x+x^2}{2 e^{-1-x}+x}\right )}{6 e^{4-2 x} x^2+5 e^{5-x} x^3+e^6 x^4+\left (-12 e^{1-2 x} x^2-10 e^{2-x} x^3-2 e^3 x^4\right ) \log \left (\frac {3 e^{-1-x} x+x^2}{2 e^{-1-x}+x}\right )+\left (6 e^{-2-2 x} x^2+5 e^{-1-x} x^3+x^4\right ) \log ^2\left (\frac {3 e^{-1-x} x+x^2}{2 e^{-1-x}+x}\right )} \, dx=\frac {- 3 x + 3 \log {\left (x \right )}}{x \log {\left (\frac {x^{2} + 3 x e^{- x - 1}}{x + 2 e^{- x - 1}} \right )} - x e^{3}} \]
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Time = 0.69 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.23 \[ \int \frac {-3 e^3 x^2+3 x^3+e^{-2-2 x} \left (-18 e^3+18 x\right )+e^{-1-x} \left (-15 e^3 x+12 x^2-3 x^3\right )+\left (e^{-2-2 x} \left (-18+18 e^3\right )-3 x^2+3 e^3 x^2+e^{-1-x} \left (-12 x+15 e^3 x+3 x^2\right )\right ) \log (x)+\left (18 e^{-2-2 x}+15 e^{-1-x} x+3 x^2+\left (-18 e^{-2-2 x}-15 e^{-1-x} x-3 x^2\right ) \log (x)\right ) \log \left (\frac {3 e^{-1-x} x+x^2}{2 e^{-1-x}+x}\right )}{6 e^{4-2 x} x^2+5 e^{5-x} x^3+e^6 x^4+\left (-12 e^{1-2 x} x^2-10 e^{2-x} x^3-2 e^3 x^4\right ) \log \left (\frac {3 e^{-1-x} x+x^2}{2 e^{-1-x}+x}\right )+\left (6 e^{-2-2 x} x^2+5 e^{-1-x} x^3+x^4\right ) \log ^2\left (\frac {3 e^{-1-x} x+x^2}{2 e^{-1-x}+x}\right )} \, dx=\frac {3 \, {\left (x - \log \left (x\right )\right )}}{x e^{3} - x \log \left (x e^{\left (x + 1\right )} + 3\right ) + x \log \left (x e^{\left (x + 1\right )} + 2\right ) - x \log \left (x\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 1129 vs. \(2 (33) = 66\).
Time = 3.21 (sec) , antiderivative size = 1129, normalized size of antiderivative = 32.26 \[ \int \frac {-3 e^3 x^2+3 x^3+e^{-2-2 x} \left (-18 e^3+18 x\right )+e^{-1-x} \left (-15 e^3 x+12 x^2-3 x^3\right )+\left (e^{-2-2 x} \left (-18+18 e^3\right )-3 x^2+3 e^3 x^2+e^{-1-x} \left (-12 x+15 e^3 x+3 x^2\right )\right ) \log (x)+\left (18 e^{-2-2 x}+15 e^{-1-x} x+3 x^2+\left (-18 e^{-2-2 x}-15 e^{-1-x} x-3 x^2\right ) \log (x)\right ) \log \left (\frac {3 e^{-1-x} x+x^2}{2 e^{-1-x}+x}\right )}{6 e^{4-2 x} x^2+5 e^{5-x} x^3+e^6 x^4+\left (-12 e^{1-2 x} x^2-10 e^{2-x} x^3-2 e^3 x^4\right ) \log \left (\frac {3 e^{-1-x} x+x^2}{2 e^{-1-x}+x}\right )+\left (6 e^{-2-2 x} x^2+5 e^{-1-x} x^3+x^4\right ) \log ^2\left (\frac {3 e^{-1-x} x+x^2}{2 e^{-1-x}+x}\right )} \, dx=\text {Too large to display} \]
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Timed out. \[ \int \frac {-3 e^3 x^2+3 x^3+e^{-2-2 x} \left (-18 e^3+18 x\right )+e^{-1-x} \left (-15 e^3 x+12 x^2-3 x^3\right )+\left (e^{-2-2 x} \left (-18+18 e^3\right )-3 x^2+3 e^3 x^2+e^{-1-x} \left (-12 x+15 e^3 x+3 x^2\right )\right ) \log (x)+\left (18 e^{-2-2 x}+15 e^{-1-x} x+3 x^2+\left (-18 e^{-2-2 x}-15 e^{-1-x} x-3 x^2\right ) \log (x)\right ) \log \left (\frac {3 e^{-1-x} x+x^2}{2 e^{-1-x}+x}\right )}{6 e^{4-2 x} x^2+5 e^{5-x} x^3+e^6 x^4+\left (-12 e^{1-2 x} x^2-10 e^{2-x} x^3-2 e^3 x^4\right ) \log \left (\frac {3 e^{-1-x} x+x^2}{2 e^{-1-x}+x}\right )+\left (6 e^{-2-2 x} x^2+5 e^{-1-x} x^3+x^4\right ) \log ^2\left (\frac {3 e^{-1-x} x+x^2}{2 e^{-1-x}+x}\right )} \, dx=\int \frac {\ln \left (x\right )\,\left ({\mathrm {e}}^{-2\,x-2}\,\left (18\,{\mathrm {e}}^3-18\right )+3\,x^2\,{\mathrm {e}}^3+{\mathrm {e}}^{-x-1}\,\left (15\,x\,{\mathrm {e}}^3-12\,x+3\,x^2\right )-3\,x^2\right )-{\mathrm {e}}^{-x-1}\,\left (3\,x^3-12\,x^2+15\,{\mathrm {e}}^3\,x\right )+\ln \left (\frac {3\,x\,{\mathrm {e}}^{-x-1}+x^2}{x+2\,{\mathrm {e}}^{-x-1}}\right )\,\left (18\,{\mathrm {e}}^{-2\,x-2}-\ln \left (x\right )\,\left (18\,{\mathrm {e}}^{-2\,x-2}+15\,x\,{\mathrm {e}}^{-x-1}+3\,x^2\right )+15\,x\,{\mathrm {e}}^{-x-1}+3\,x^2\right )-3\,x^2\,{\mathrm {e}}^3+3\,x^3+{\mathrm {e}}^{-2\,x-2}\,\left (18\,x-18\,{\mathrm {e}}^3\right )}{{\ln \left (\frac {3\,x\,{\mathrm {e}}^{-x-1}+x^2}{x+2\,{\mathrm {e}}^{-x-1}}\right )}^2\,\left (5\,x^3\,{\mathrm {e}}^{-x-1}+6\,x^2\,{\mathrm {e}}^{-2\,x-2}+x^4\right )+x^4\,{\mathrm {e}}^6-\ln \left (\frac {3\,x\,{\mathrm {e}}^{-x-1}+x^2}{x+2\,{\mathrm {e}}^{-x-1}}\right )\,\left (2\,x^4\,{\mathrm {e}}^3+12\,x^2\,{\mathrm {e}}^{1-2\,x}+10\,x^3\,{\mathrm {e}}^{2-x}\right )+6\,x^2\,{\mathrm {e}}^{4-2\,x}+5\,x^3\,{\mathrm {e}}^{5-x}} \,d x \]
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