Integrand size = 125, antiderivative size = 45 \[ \int \frac {5^{\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} \left (-900 x+20000 x^3+20000 x^4+\left (-1800 x+900 x^2-40000 x^4-20000 x^5\right ) \log (5 x)\right )}{81-3600 x^2-3600 x^3+40000 x^4+80000 x^5+40000 x^6} \, dx=5^{\frac {e^{-x}}{2-\frac {9}{100 x^2}+2 x}} x^{\frac {e^{-x}}{2-\frac {9}{100 x^2}+2 x}} \]
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\[ \int \frac {5^{\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} \left (-900 x+20000 x^3+20000 x^4+\left (-1800 x+900 x^2-40000 x^4-20000 x^5\right ) \log (5 x)\right )}{81-3600 x^2-3600 x^3+40000 x^4+80000 x^5+40000 x^6} \, dx=\int \frac {5^{\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} \left (-900 x+20000 x^3+20000 x^4+\left (-1800 x+900 x^2-40000 x^4-20000 x^5\right ) \log (5 x)\right )}{81-3600 x^2-3600 x^3+40000 x^4+80000 x^5+40000 x^6} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {5^{\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} \left (-900 x+20000 x^3+20000 x^4+\left (-1800 x+900 x^2-40000 x^4-20000 x^5\right ) \log (5 x)\right )}{\left (9-200 x^2-200 x^3\right )^2} \, dx \\ & = \int \left (\frac {4\ 5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3}-\frac {4\ 5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} \left (18-9 x+400 x^3+200 x^4\right ) \log (5 x)}{\left (-9+200 x^2+200 x^3\right )^2}\right ) \, dx \\ & = 4 \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx-4 \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} \left (18-9 x+400 x^3+200 x^4\right ) \log (5 x)}{\left (-9+200 x^2+200 x^3\right )^2} \, dx \\ & = 4 \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx+4 \int \frac {27 \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{\left (-9+200 x^2+200 x^3\right )^2} \, dx-8 \int \frac {5^{4+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{3+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{\left (-9+200 x^2+200 x^3\right )^2} \, dx+\int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx+\int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx}{x} \, dx-(4 \log (5 x)) \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx-(4 \log (5 x)) \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx+(32 \log (5 x)) \int \frac {5^{4+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{3+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{\left (-9+200 x^2+200 x^3\right )^2} \, dx-(108 \log (5 x)) \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{\left (-9+200 x^2+200 x^3\right )^2} \, dx \\ & = 4 \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx+4 \int \left (\frac {27 \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{\left (-9+200 x^2+200 x^3\right )^2} \, dx-8 \int \frac {5^{4+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{3+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{\left (-9+200 x^2+200 x^3\right )^2} \, dx+\int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx}{x}+\frac {\int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx}{x}\right ) \, dx-(4 \log (5 x)) \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx-(4 \log (5 x)) \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx+(32 \log (5 x)) \int \frac {5^{4+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{3+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{\left (-9+200 x^2+200 x^3\right )^2} \, dx-(108 \log (5 x)) \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{\left (-9+200 x^2+200 x^3\right )^2} \, dx \\ & = 4 \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx+4 \int \frac {27 \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{\left (-9+200 x^2+200 x^3\right )^2} \, dx-8 \int \frac {5^{4+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{3+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{\left (-9+200 x^2+200 x^3\right )^2} \, dx+\int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx}{x} \, dx+4 \int \frac {\int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx}{x} \, dx-(4 \log (5 x)) \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx-(4 \log (5 x)) \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx+(32 \log (5 x)) \int \frac {5^{4+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{3+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{\left (-9+200 x^2+200 x^3\right )^2} \, dx-(108 \log (5 x)) \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{\left (-9+200 x^2+200 x^3\right )^2} \, dx \\ & = 4 \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx+4 \int \left (\frac {27 \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{\left (-9+200 x^2+200 x^3\right )^2} \, dx-8 \int \frac {5^{4+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{3+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{\left (-9+200 x^2+200 x^3\right )^2} \, dx}{x}+\frac {\int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx}{x}\right ) \, dx+4 \int \frac {\int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx}{x} \, dx-(4 \log (5 x)) \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx-(4 \log (5 x)) \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx+(32 \log (5 x)) \int \frac {5^{4+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{3+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{\left (-9+200 x^2+200 x^3\right )^2} \, dx-(108 \log (5 x)) \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{\left (-9+200 x^2+200 x^3\right )^2} \, dx \\ & = 4 \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx+4 \int \frac {27 \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{\left (-9+200 x^2+200 x^3\right )^2} \, dx-8 \int \frac {5^{4+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{3+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{\left (-9+200 x^2+200 x^3\right )^2} \, dx}{x} \, dx+4 \int \frac {\int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx}{x} \, dx+4 \int \frac {\int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx}{x} \, dx-(4 \log (5 x)) \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx-(4 \log (5 x)) \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx+(32 \log (5 x)) \int \frac {5^{4+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{3+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{\left (-9+200 x^2+200 x^3\right )^2} \, dx-(108 \log (5 x)) \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{\left (-9+200 x^2+200 x^3\right )^2} \, dx \\ & = 4 \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx+4 \int \left (\frac {27 \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{\left (-9+200 x^2+200 x^3\right )^2} \, dx}{x}-\frac {8 \int \frac {5^{4+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{3+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{\left (-9+200 x^2+200 x^3\right )^2} \, dx}{x}\right ) \, dx+4 \int \frac {\int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx}{x} \, dx+4 \int \frac {\int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx}{x} \, dx-(4 \log (5 x)) \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx-(4 \log (5 x)) \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx+(32 \log (5 x)) \int \frac {5^{4+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{3+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{\left (-9+200 x^2+200 x^3\right )^2} \, dx-(108 \log (5 x)) \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{\left (-9+200 x^2+200 x^3\right )^2} \, dx \\ & = 4 \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx+4 \int \frac {\int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx}{x} \, dx+4 \int \frac {\int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx}{x} \, dx-32 \int \frac {\int \frac {5^{4+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{3+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{\left (-9+200 x^2+200 x^3\right )^2} \, dx}{x} \, dx+108 \int \frac {\int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{\left (-9+200 x^2+200 x^3\right )^2} \, dx}{x} \, dx-(4 \log (5 x)) \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx-(4 \log (5 x)) \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{-9+200 x^2+200 x^3} \, dx+(32 \log (5 x)) \int \frac {5^{4+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{3+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{\left (-9+200 x^2+200 x^3\right )^2} \, dx-(108 \log (5 x)) \int \frac {5^{2+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{1+\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}}}{\left (-9+200 x^2+200 x^3\right )^2} \, dx \\ \end{align*}
\[ \int \frac {5^{\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} \left (-900 x+20000 x^3+20000 x^4+\left (-1800 x+900 x^2-40000 x^4-20000 x^5\right ) \log (5 x)\right )}{81-3600 x^2-3600 x^3+40000 x^4+80000 x^5+40000 x^6} \, dx=\int \frac {5^{\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} \left (-900 x+20000 x^3+20000 x^4+\left (-1800 x+900 x^2-40000 x^4-20000 x^5\right ) \log (5 x)\right )}{81-3600 x^2-3600 x^3+40000 x^4+80000 x^5+40000 x^6} \, dx \]
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Time = 161.96 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.62
method | result | size |
risch | \(\left (5 x \right )^{\frac {100 x^{2} {\mathrm e}^{-x}}{200 x^{3}+200 x^{2}-9}}\) | \(28\) |
parallelrisch | \({\mathrm e}^{\frac {100 x^{2} \ln \left (5 x \right ) {\mathrm e}^{-x}}{200 x^{3}+200 x^{2}-9}}\) | \(29\) |
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Time = 0.27 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.60 \[ \int \frac {5^{\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} \left (-900 x+20000 x^3+20000 x^4+\left (-1800 x+900 x^2-40000 x^4-20000 x^5\right ) \log (5 x)\right )}{81-3600 x^2-3600 x^3+40000 x^4+80000 x^5+40000 x^6} \, dx=\left (5 \, x\right )^{\frac {100 \, x^{2} e^{\left (-x\right )}}{200 \, x^{3} + 200 \, x^{2} - 9}} \]
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Time = 0.47 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.58 \[ \int \frac {5^{\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} \left (-900 x+20000 x^3+20000 x^4+\left (-1800 x+900 x^2-40000 x^4-20000 x^5\right ) \log (5 x)\right )}{81-3600 x^2-3600 x^3+40000 x^4+80000 x^5+40000 x^6} \, dx=e^{\frac {100 x^{2} e^{- x} \log {\left (5 x \right )}}{200 x^{3} + 200 x^{2} - 9}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 52 vs. \(2 (22) = 44\).
Time = 0.42 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.16 \[ \int \frac {5^{\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} \left (-900 x+20000 x^3+20000 x^4+\left (-1800 x+900 x^2-40000 x^4-20000 x^5\right ) \log (5 x)\right )}{81-3600 x^2-3600 x^3+40000 x^4+80000 x^5+40000 x^6} \, dx=e^{\left (\frac {100 \, x^{2} e^{\left (-x\right )} \log \left (5\right )}{200 \, x^{3} + 200 \, x^{2} - 9} + \frac {100 \, x^{2} e^{\left (-x\right )} \log \left (x\right )}{200 \, x^{3} + 200 \, x^{2} - 9}\right )} \]
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Time = 3.32 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.60 \[ \int \frac {5^{\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} \left (-900 x+20000 x^3+20000 x^4+\left (-1800 x+900 x^2-40000 x^4-20000 x^5\right ) \log (5 x)\right )}{81-3600 x^2-3600 x^3+40000 x^4+80000 x^5+40000 x^6} \, dx=\left (5 \, x\right )^{\frac {100 \, x^{2} e^{\left (-x\right )}}{200 \, x^{3} + 200 \, x^{2} - 9}} \]
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Time = 13.31 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.13 \[ \int \frac {5^{\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} e^{-x} x^{\frac {100 e^{-x} x^2}{-9+200 x^2+200 x^3}} \left (-900 x+20000 x^3+20000 x^4+\left (-1800 x+900 x^2-40000 x^4-20000 x^5\right ) \log (5 x)\right )}{81-3600 x^2-3600 x^3+40000 x^4+80000 x^5+40000 x^6} \, dx=5^{\frac {100\,x^2\,{\mathrm {e}}^{-x}}{200\,x^3+200\,x^2-9}}\,x^{\frac {100\,x^2\,{\mathrm {e}}^{-x}}{200\,x^3+200\,x^2-9}} \]
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