Integrand size = 172, antiderivative size = 31 \[ \int \frac {-3 x^4+3 e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^3 \log (x)+e^{\frac {1}{3} \left (-5+\log \left (-x+e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} \log (x)\right )\right )} \left (e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^2-x^3+e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} \left (-50-10 e^3 x\right ) \log (x)\right )}{-3 x^4+3 e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^3 \log (x)} \, dx=e^{\frac {1}{3} \left (-5+\log \left (-x+e^{\left (e^3+\frac {5}{x}\right )^2} \log (x)\right )\right )}+x \]
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\[ \int \frac {-3 x^4+3 e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^3 \log (x)+e^{\frac {1}{3} \left (-5+\log \left (-x+e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} \log (x)\right )\right )} \left (e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^2-x^3+e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} \left (-50-10 e^3 x\right ) \log (x)\right )}{-3 x^4+3 e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^3 \log (x)} \, dx=\int \frac {-3 x^4+3 e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^3 \log (x)+\exp \left (\frac {1}{3} \left (-5+\log \left (-x+e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} \log (x)\right )\right )\right ) \left (e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^2-x^3+e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} \left (-50-10 e^3 x\right ) \log (x)\right )}{-3 x^4+3 e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^3 \log (x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {3 x^4-3 e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^3 \log (x)-\exp \left (\frac {1}{3} \left (-5+\log \left (-x+e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} \log (x)\right )\right )\right ) \left (e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^2-x^3+e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} \left (-50-10 e^3 x\right ) \log (x)\right )}{3 x^3 \left (x-e^{\frac {\left (5+e^3 x\right )^2}{x^2}} \log (x)\right )} \, dx \\ & = \frac {1}{3} \int \frac {3 x^4-3 e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^3 \log (x)-\exp \left (\frac {1}{3} \left (-5+\log \left (-x+e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} \log (x)\right )\right )\right ) \left (e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^2-x^3+e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} \left (-50-10 e^3 x\right ) \log (x)\right )}{x^3 \left (x-e^{\frac {\left (5+e^3 x\right )^2}{x^2}} \log (x)\right )} \, dx \\ & = \frac {1}{3} \int \left (3-\frac {-e^{\frac {\left (5+e^3 x\right )^2}{x^2}} x^2+x^3+50 e^{\frac {\left (5+e^3 x\right )^2}{x^2}} \log (x)+10 e^{3+\frac {\left (5+e^3 x\right )^2}{x^2}} x \log (x)}{e^{5/3} x^3 \left (-x+e^{\frac {\left (5+e^3 x\right )^2}{x^2}} \log (x)\right )^{2/3}}\right ) \, dx \\ & = x-\frac {\int \frac {-e^{\frac {\left (5+e^3 x\right )^2}{x^2}} x^2+x^3+50 e^{\frac {\left (5+e^3 x\right )^2}{x^2}} \log (x)+10 e^{3+\frac {\left (5+e^3 x\right )^2}{x^2}} x \log (x)}{x^3 \left (-x+e^{\frac {\left (5+e^3 x\right )^2}{x^2}} \log (x)\right )^{2/3}} \, dx}{3 e^{5/3}} \\ & = x-\frac {\int \left (\frac {1}{\left (-x+e^{\frac {\left (5+e^3 x\right )^2}{x^2}} \log (x)\right )^{2/3}}-\frac {e^{\frac {\left (5+e^3 x\right )^2}{x^2}} \left (x^2-50 \log (x)-10 e^3 x \log (x)\right )}{x^3 \left (-x+e^{\frac {\left (5+e^3 x\right )^2}{x^2}} \log (x)\right )^{2/3}}\right ) \, dx}{3 e^{5/3}} \\ & = x-\frac {\int \frac {1}{\left (-x+e^{\frac {\left (5+e^3 x\right )^2}{x^2}} \log (x)\right )^{2/3}} \, dx}{3 e^{5/3}}+\frac {\int \frac {e^{\frac {\left (5+e^3 x\right )^2}{x^2}} \left (x^2-50 \log (x)-10 e^3 x \log (x)\right )}{x^3 \left (-x+e^{\frac {\left (5+e^3 x\right )^2}{x^2}} \log (x)\right )^{2/3}} \, dx}{3 e^{5/3}} \\ & = x-\frac {\int \frac {1}{\left (-x+e^{\frac {\left (5+e^3 x\right )^2}{x^2}} \log (x)\right )^{2/3}} \, dx}{3 e^{5/3}}+\frac {\int \left (\frac {e^{\frac {\left (5+e^3 x\right )^2}{x^2}}}{x \left (-x+e^{\frac {\left (5+e^3 x\right )^2}{x^2}} \log (x)\right )^{2/3}}-\frac {10 e^{\frac {\left (5+e^3 x\right )^2}{x^2}} \left (5+e^3 x\right ) \log (x)}{x^3 \left (-x+e^{\frac {\left (5+e^3 x\right )^2}{x^2}} \log (x)\right )^{2/3}}\right ) \, dx}{3 e^{5/3}} \\ & = x-\frac {\int \frac {1}{\left (-x+e^{\frac {\left (5+e^3 x\right )^2}{x^2}} \log (x)\right )^{2/3}} \, dx}{3 e^{5/3}}+\frac {\int \frac {e^{\frac {\left (5+e^3 x\right )^2}{x^2}}}{x \left (-x+e^{\frac {\left (5+e^3 x\right )^2}{x^2}} \log (x)\right )^{2/3}} \, dx}{3 e^{5/3}}-\frac {10 \int \frac {e^{\frac {\left (5+e^3 x\right )^2}{x^2}} \left (5+e^3 x\right ) \log (x)}{x^3 \left (-x+e^{\frac {\left (5+e^3 x\right )^2}{x^2}} \log (x)\right )^{2/3}} \, dx}{3 e^{5/3}} \\ & = x-\frac {\int \frac {1}{\left (-x+e^{\frac {\left (5+e^3 x\right )^2}{x^2}} \log (x)\right )^{2/3}} \, dx}{3 e^{5/3}}+\frac {\int \frac {e^{\frac {\left (5+e^3 x\right )^2}{x^2}}}{x \left (-x+e^{\frac {\left (5+e^3 x\right )^2}{x^2}} \log (x)\right )^{2/3}} \, dx}{3 e^{5/3}}-\frac {10 \int \left (\frac {5 e^{\frac {\left (5+e^3 x\right )^2}{x^2}} \log (x)}{x^3 \left (-x+e^{\frac {\left (5+e^3 x\right )^2}{x^2}} \log (x)\right )^{2/3}}+\frac {e^{3+\frac {\left (5+e^3 x\right )^2}{x^2}} \log (x)}{x^2 \left (-x+e^{\frac {\left (5+e^3 x\right )^2}{x^2}} \log (x)\right )^{2/3}}\right ) \, dx}{3 e^{5/3}} \\ & = x-\frac {\int \frac {1}{\left (-x+e^{\frac {\left (5+e^3 x\right )^2}{x^2}} \log (x)\right )^{2/3}} \, dx}{3 e^{5/3}}+\frac {\int \frac {e^{\frac {\left (5+e^3 x\right )^2}{x^2}}}{x \left (-x+e^{\frac {\left (5+e^3 x\right )^2}{x^2}} \log (x)\right )^{2/3}} \, dx}{3 e^{5/3}}-\frac {10 \int \frac {e^{3+\frac {\left (5+e^3 x\right )^2}{x^2}} \log (x)}{x^2 \left (-x+e^{\frac {\left (5+e^3 x\right )^2}{x^2}} \log (x)\right )^{2/3}} \, dx}{3 e^{5/3}}-\frac {50 \int \frac {e^{\frac {\left (5+e^3 x\right )^2}{x^2}} \log (x)}{x^3 \left (-x+e^{\frac {\left (5+e^3 x\right )^2}{x^2}} \log (x)\right )^{2/3}} \, dx}{3 e^{5/3}} \\ \end{align*}
Time = 0.91 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.32 \[ \int \frac {-3 x^4+3 e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^3 \log (x)+e^{\frac {1}{3} \left (-5+\log \left (-x+e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} \log (x)\right )\right )} \left (e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^2-x^3+e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} \left (-50-10 e^3 x\right ) \log (x)\right )}{-3 x^4+3 e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^3 \log (x)} \, dx=\frac {1}{3} \left (3 x+\frac {3 \sqrt [3]{-x+e^{\frac {\left (5+e^3 x\right )^2}{x^2}} \log (x)}}{e^{5/3}}\right ) \]
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\[\int \frac {\left (\left (-10 x \,{\mathrm e}^{3}-50\right ) {\mathrm e}^{\frac {x^{2} {\mathrm e}^{6}+10 x \,{\mathrm e}^{3}+25}{x^{2}}} \ln \left (x \right )+x^{2} {\mathrm e}^{\frac {x^{2} {\mathrm e}^{6}+10 x \,{\mathrm e}^{3}+25}{x^{2}}}-x^{3}\right ) {\mathrm e}^{\frac {\ln \left ({\mathrm e}^{\frac {x^{2} {\mathrm e}^{6}+10 x \,{\mathrm e}^{3}+25}{x^{2}}} \ln \left (x \right )-x \right )}{3}-\frac {5}{3}}+3 x^{3} {\mathrm e}^{\frac {x^{2} {\mathrm e}^{6}+10 x \,{\mathrm e}^{3}+25}{x^{2}}} \ln \left (x \right )-3 x^{4}}{3 x^{3} {\mathrm e}^{\frac {x^{2} {\mathrm e}^{6}+10 x \,{\mathrm e}^{3}+25}{x^{2}}} \ln \left (x \right )-3 x^{4}}d x\]
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Exception generated. \[ \int \frac {-3 x^4+3 e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^3 \log (x)+e^{\frac {1}{3} \left (-5+\log \left (-x+e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} \log (x)\right )\right )} \left (e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^2-x^3+e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} \left (-50-10 e^3 x\right ) \log (x)\right )}{-3 x^4+3 e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^3 \log (x)} \, dx=\text {Exception raised: TypeError} \]
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Timed out. \[ \int \frac {-3 x^4+3 e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^3 \log (x)+e^{\frac {1}{3} \left (-5+\log \left (-x+e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} \log (x)\right )\right )} \left (e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^2-x^3+e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} \left (-50-10 e^3 x\right ) \log (x)\right )}{-3 x^4+3 e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^3 \log (x)} \, dx=\text {Timed out} \]
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Time = 0.30 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.06 \[ \int \frac {-3 x^4+3 e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^3 \log (x)+e^{\frac {1}{3} \left (-5+\log \left (-x+e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} \log (x)\right )\right )} \left (e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^2-x^3+e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} \left (-50-10 e^3 x\right ) \log (x)\right )}{-3 x^4+3 e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^3 \log (x)} \, dx={\left (x e^{\frac {5}{3}} + {\left (e^{\left (\frac {10 \, e^{3}}{x} + \frac {25}{x^{2}} + e^{6}\right )} \log \left (x\right ) - x\right )}^{\frac {1}{3}}\right )} e^{\left (-\frac {5}{3}\right )} \]
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\[ \int \frac {-3 x^4+3 e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^3 \log (x)+e^{\frac {1}{3} \left (-5+\log \left (-x+e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} \log (x)\right )\right )} \left (e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^2-x^3+e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} \left (-50-10 e^3 x\right ) \log (x)\right )}{-3 x^4+3 e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^3 \log (x)} \, dx=\int { \frac {3 \, x^{3} e^{\left (\frac {x^{2} e^{6} + 10 \, x e^{3} + 25}{x^{2}}\right )} \log \left (x\right ) - 3 \, x^{4} - {\left (x^{3} - x^{2} e^{\left (\frac {x^{2} e^{6} + 10 \, x e^{3} + 25}{x^{2}}\right )} + 10 \, {\left (x e^{3} + 5\right )} e^{\left (\frac {x^{2} e^{6} + 10 \, x e^{3} + 25}{x^{2}}\right )} \log \left (x\right )\right )} e^{\left (\frac {1}{3} \, \log \left (e^{\left (\frac {x^{2} e^{6} + 10 \, x e^{3} + 25}{x^{2}}\right )} \log \left (x\right ) - x\right ) - \frac {5}{3}\right )}}{3 \, {\left (x^{3} e^{\left (\frac {x^{2} e^{6} + 10 \, x e^{3} + 25}{x^{2}}\right )} \log \left (x\right ) - x^{4}\right )}} \,d x } \]
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Timed out. \[ \int \frac {-3 x^4+3 e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^3 \log (x)+e^{\frac {1}{3} \left (-5+\log \left (-x+e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} \log (x)\right )\right )} \left (e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^2-x^3+e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} \left (-50-10 e^3 x\right ) \log (x)\right )}{-3 x^4+3 e^{\frac {25+10 e^3 x+e^6 x^2}{x^2}} x^3 \log (x)} \, dx=\int \frac {{\mathrm {e}}^{\frac {\ln \left ({\mathrm {e}}^{\frac {{\mathrm {e}}^6\,x^2+10\,{\mathrm {e}}^3\,x+25}{x^2}}\,\ln \left (x\right )-x\right )}{3}-\frac {5}{3}}\,\left (x^3-x^2\,{\mathrm {e}}^{\frac {{\mathrm {e}}^6\,x^2+10\,{\mathrm {e}}^3\,x+25}{x^2}}+{\mathrm {e}}^{\frac {{\mathrm {e}}^6\,x^2+10\,{\mathrm {e}}^3\,x+25}{x^2}}\,\ln \left (x\right )\,\left (10\,x\,{\mathrm {e}}^3+50\right )\right )+3\,x^4-3\,x^3\,{\mathrm {e}}^{\frac {{\mathrm {e}}^6\,x^2+10\,{\mathrm {e}}^3\,x+25}{x^2}}\,\ln \left (x\right )}{3\,x^4-3\,x^3\,{\mathrm {e}}^{\frac {{\mathrm {e}}^6\,x^2+10\,{\mathrm {e}}^3\,x+25}{x^2}}\,\ln \left (x\right )} \,d x \]
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