Integrand size = 251, antiderivative size = 26 \[ \int \frac {e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}} \left (-50+\left (-100-10 x^3\right ) \log (x)-10 x^3 \log ^2(x)+2 x^6 \log ^3(x)\right )}{\left (-100 x^5 \log ^3(x)+20 e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}} x^5 \log ^3(x)+\log \left (5-e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}}\right ) \left (-5 x^5 \log ^3(x)+e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}} x^5 \log ^3(x)\right )\right ) \log \left (20+\log \left (5-e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}}\right )\right )} \, dx=\log \left (\log \left (20+\log \left (5-e^{-5+\left (x+\frac {5}{x^2 \log (x)}\right )^2}\right )\right )\right ) \]
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\[ \int \frac {e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}} \left (-50+\left (-100-10 x^3\right ) \log (x)-10 x^3 \log ^2(x)+2 x^6 \log ^3(x)\right )}{\left (-100 x^5 \log ^3(x)+20 e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}} x^5 \log ^3(x)+\log \left (5-e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}}\right ) \left (-5 x^5 \log ^3(x)+e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}} x^5 \log ^3(x)\right )\right ) \log \left (20+\log \left (5-e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}}\right )\right )} \, dx=\int \frac {\exp \left (\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}\right ) \left (-50+\left (-100-10 x^3\right ) \log (x)-10 x^3 \log ^2(x)+2 x^6 \log ^3(x)\right )}{\left (-100 x^5 \log ^3(x)+20 \exp \left (\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}\right ) x^5 \log ^3(x)+\log \left (5-\exp \left (\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}\right )\right ) \left (-5 x^5 \log ^3(x)+\exp \left (\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}\right ) x^5 \log ^3(x)\right )\right ) \log \left (20+\log \left (5-\exp \left (\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}\right )\right )\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {2 e^{\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}} \left (25+5 \left (10+x^3\right ) \log (x)+5 x^3 \log ^2(x)-x^6 \log ^3(x)\right )}{\left (5 e^5-e^{\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right ) x^5 \left (20+\log \left (5-e^{-5+\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right )\right ) \log ^3(x) \log \left (20+\log \left (5-e^{-5+\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right )\right )} \, dx \\ & = 2 \int \frac {e^{\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}} \left (25+5 \left (10+x^3\right ) \log (x)+5 x^3 \log ^2(x)-x^6 \log ^3(x)\right )}{\left (5 e^5-e^{\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right ) x^5 \left (20+\log \left (5-e^{-5+\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right )\right ) \log ^3(x) \log \left (20+\log \left (5-e^{-5+\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right )\right )} \, dx \\ & = 2 \int \left (\frac {e^{\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}} x}{\left (-5 e^5+e^{\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right ) \left (20+\log \left (5-e^{-5+\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right )\right ) \log \left (20+\log \left (5-e^{-5+\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right )\right )}-\frac {25 e^{\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}}{\left (-5 e^5+e^{\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right ) x^5 \left (20+\log \left (5-e^{-5+\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right )\right ) \log ^3(x) \log \left (20+\log \left (5-e^{-5+\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right )\right )}-\frac {50 e^{\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}}{\left (-5 e^5+e^{\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right ) x^5 \left (20+\log \left (5-e^{-5+\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right )\right ) \log ^2(x) \log \left (20+\log \left (5-e^{-5+\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right )\right )}-\frac {5 e^{\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}}{\left (-5 e^5+e^{\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right ) x^2 \left (20+\log \left (5-e^{-5+\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right )\right ) \log ^2(x) \log \left (20+\log \left (5-e^{-5+\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right )\right )}-\frac {5 e^{\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}}{\left (-5 e^5+e^{\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right ) x^2 \left (20+\log \left (5-e^{-5+\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right )\right ) \log (x) \log \left (20+\log \left (5-e^{-5+\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right )\right )}\right ) \, dx \\ & = 2 \int \frac {e^{\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}} x}{\left (-5 e^5+e^{\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right ) \left (20+\log \left (5-e^{-5+\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right )\right ) \log \left (20+\log \left (5-e^{-5+\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right )\right )} \, dx-10 \int \frac {e^{\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}}{\left (-5 e^5+e^{\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right ) x^2 \left (20+\log \left (5-e^{-5+\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right )\right ) \log ^2(x) \log \left (20+\log \left (5-e^{-5+\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right )\right )} \, dx-10 \int \frac {e^{\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}}{\left (-5 e^5+e^{\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right ) x^2 \left (20+\log \left (5-e^{-5+\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right )\right ) \log (x) \log \left (20+\log \left (5-e^{-5+\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right )\right )} \, dx-50 \int \frac {e^{\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}}{\left (-5 e^5+e^{\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right ) x^5 \left (20+\log \left (5-e^{-5+\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right )\right ) \log ^3(x) \log \left (20+\log \left (5-e^{-5+\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right )\right )} \, dx-100 \int \frac {e^{\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}}{\left (-5 e^5+e^{\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right ) x^5 \left (20+\log \left (5-e^{-5+\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right )\right ) \log ^2(x) \log \left (20+\log \left (5-e^{-5+\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right )\right )} \, dx \\ \end{align*}
Time = 0.20 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.19 \[ \int \frac {e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}} \left (-50+\left (-100-10 x^3\right ) \log (x)-10 x^3 \log ^2(x)+2 x^6 \log ^3(x)\right )}{\left (-100 x^5 \log ^3(x)+20 e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}} x^5 \log ^3(x)+\log \left (5-e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}}\right ) \left (-5 x^5 \log ^3(x)+e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}} x^5 \log ^3(x)\right )\right ) \log \left (20+\log \left (5-e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}}\right )\right )} \, dx=\log \left (\log \left (20+\log \left (5-e^{-5+\frac {\left (5+x^3 \log (x)\right )^2}{x^4 \log ^2(x)}}\right )\right )\right ) \]
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Time = 0.27 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.73
\[\ln \left (\ln \left (\ln \left (-{\mathrm e}^{\frac {x^{6} \ln \left (x \right )^{2}-5 x^{4} \ln \left (x \right )^{2}+10 x^{3} \ln \left (x \right )+25}{x^{4} \ln \left (x \right )^{2}}}+5\right )+20\right )\right )\]
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Time = 0.26 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.58 \[ \int \frac {e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}} \left (-50+\left (-100-10 x^3\right ) \log (x)-10 x^3 \log ^2(x)+2 x^6 \log ^3(x)\right )}{\left (-100 x^5 \log ^3(x)+20 e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}} x^5 \log ^3(x)+\log \left (5-e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}}\right ) \left (-5 x^5 \log ^3(x)+e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}} x^5 \log ^3(x)\right )\right ) \log \left (20+\log \left (5-e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}}\right )\right )} \, dx=\log \left (\log \left (\log \left (-e^{\left (\frac {10 \, x^{3} \log \left (x\right ) + {\left (x^{6} - 5 \, x^{4}\right )} \log \left (x\right )^{2} + 25}{x^{4} \log \left (x\right )^{2}}\right )} + 5\right ) + 20\right )\right ) \]
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Timed out. \[ \int \frac {e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}} \left (-50+\left (-100-10 x^3\right ) \log (x)-10 x^3 \log ^2(x)+2 x^6 \log ^3(x)\right )}{\left (-100 x^5 \log ^3(x)+20 e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}} x^5 \log ^3(x)+\log \left (5-e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}}\right ) \left (-5 x^5 \log ^3(x)+e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}} x^5 \log ^3(x)\right )\right ) \log \left (20+\log \left (5-e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}}\right )\right )} \, dx=\text {Timed out} \]
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Time = 0.41 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.35 \[ \int \frac {e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}} \left (-50+\left (-100-10 x^3\right ) \log (x)-10 x^3 \log ^2(x)+2 x^6 \log ^3(x)\right )}{\left (-100 x^5 \log ^3(x)+20 e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}} x^5 \log ^3(x)+\log \left (5-e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}}\right ) \left (-5 x^5 \log ^3(x)+e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}} x^5 \log ^3(x)\right )\right ) \log \left (20+\log \left (5-e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}}\right )\right )} \, dx=\log \left (\log \left (\log \left (5 \, e^{5} - e^{\left (x^{2} + \frac {10}{x \log \left (x\right )} + \frac {25}{x^{4} \log \left (x\right )^{2}}\right )}\right ) + 15\right )\right ) \]
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Time = 0.61 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.69 \[ \int \frac {e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}} \left (-50+\left (-100-10 x^3\right ) \log (x)-10 x^3 \log ^2(x)+2 x^6 \log ^3(x)\right )}{\left (-100 x^5 \log ^3(x)+20 e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}} x^5 \log ^3(x)+\log \left (5-e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}}\right ) \left (-5 x^5 \log ^3(x)+e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}} x^5 \log ^3(x)\right )\right ) \log \left (20+\log \left (5-e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}}\right )\right )} \, dx=\log \left (\log \left (\log \left (-e^{\left (\frac {x^{6} \log \left (x\right )^{2} - 5 \, x^{4} \log \left (x\right )^{2} + 10 \, x^{3} \log \left (x\right ) + 25}{x^{4} \log \left (x\right )^{2}}\right )} + 5\right ) + 20\right )\right ) \]
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Time = 12.87 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.35 \[ \int \frac {e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}} \left (-50+\left (-100-10 x^3\right ) \log (x)-10 x^3 \log ^2(x)+2 x^6 \log ^3(x)\right )}{\left (-100 x^5 \log ^3(x)+20 e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}} x^5 \log ^3(x)+\log \left (5-e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}}\right ) \left (-5 x^5 \log ^3(x)+e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}} x^5 \log ^3(x)\right )\right ) \log \left (20+\log \left (5-e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}}\right )\right )} \, dx=\ln \left (\ln \left (\ln \left (5-{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{-5}\,{\mathrm {e}}^{\frac {10}{x\,\ln \left (x\right )}}\,{\mathrm {e}}^{\frac {25}{x^4\,{\ln \left (x\right )}^2}}\right )+20\right )\right ) \]
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