Integrand size = 106, antiderivative size = 23 \[ \int \frac {18055103407718400-268738560 x \log ^4(x)+x^2 \log ^8(x)+e^{-\frac {e^{5+x} \log ^4(x)}{-134369280+x \log ^4(x)}} \left (537477120 e^{5+x} \log ^3(x)+134369280 e^{5+x} x \log ^4(x)+e^{5+x} \left (x-x^2\right ) \log ^8(x)\right )}{18055103407718400 x-268738560 x^2 \log ^4(x)+x^3 \log ^8(x)} \, dx=e^{\frac {e^{5+x}}{-x+\frac {134369280}{\log ^4(x)}}}+\log (x) \]
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\[ \int \frac {18055103407718400-268738560 x \log ^4(x)+x^2 \log ^8(x)+e^{-\frac {e^{5+x} \log ^4(x)}{-134369280+x \log ^4(x)}} \left (537477120 e^{5+x} \log ^3(x)+134369280 e^{5+x} x \log ^4(x)+e^{5+x} \left (x-x^2\right ) \log ^8(x)\right )}{18055103407718400 x-268738560 x^2 \log ^4(x)+x^3 \log ^8(x)} \, dx=\int \frac {18055103407718400-268738560 x \log ^4(x)+x^2 \log ^8(x)+e^{-\frac {e^{5+x} \log ^4(x)}{-134369280+x \log ^4(x)}} \left (537477120 e^{5+x} \log ^3(x)+134369280 e^{5+x} x \log ^4(x)+e^{5+x} \left (x-x^2\right ) \log ^8(x)\right )}{18055103407718400 x-268738560 x^2 \log ^4(x)+x^3 \log ^8(x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {18055103407718400-268738560 x \log ^4(x)+x^2 \log ^8(x)+e^{-\frac {e^{5+x} \log ^4(x)}{-134369280+x \log ^4(x)}} \left (537477120 e^{5+x} \log ^3(x)+134369280 e^{5+x} x \log ^4(x)+e^{5+x} \left (x-x^2\right ) \log ^8(x)\right )}{x \left (134369280-x \log ^4(x)\right )^2} \, dx \\ & = \int \left (\frac {1}{x}-\frac {e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}} \log ^3(x) \left (-537477120-134369280 x \log (x)-x \log ^5(x)+x^2 \log ^5(x)\right )}{x \left (-134369280+x \log ^4(x)\right )^2}\right ) \, dx \\ & = \log (x)-\int \frac {e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}} \log ^3(x) \left (-537477120-134369280 x \log (x)-x \log ^5(x)+x^2 \log ^5(x)\right )}{x \left (-134369280+x \log ^4(x)\right )^2} \, dx \\ & = \log (x)-\int \left (\frac {e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}} (-1+x)}{x^2}-\frac {537477120 e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}} \left (33592320+x \log ^3(x)\right )}{x^2 \left (-134369280+x \log ^4(x)\right )^2}+\frac {134369280 e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}} (-2+x)}{x^2 \left (-134369280+x \log ^4(x)\right )}\right ) \, dx \\ & = \log (x)-134369280 \int \frac {e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}} (-2+x)}{x^2 \left (-134369280+x \log ^4(x)\right )} \, dx+537477120 \int \frac {e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}} \left (33592320+x \log ^3(x)\right )}{x^2 \left (-134369280+x \log ^4(x)\right )^2} \, dx-\int \frac {e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}} (-1+x)}{x^2} \, dx \\ & = \log (x)-134369280 \int \left (-\frac {2 e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}}}{x^2 \left (-134369280+x \log ^4(x)\right )}+\frac {e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}}}{x \left (-134369280+x \log ^4(x)\right )}\right ) \, dx+537477120 \int \left (\frac {33592320 e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}}}{x^2 \left (-134369280+x \log ^4(x)\right )^2}+\frac {e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}} \log ^3(x)}{x \left (-134369280+x \log ^4(x)\right )^2}\right ) \, dx-\int \left (-\frac {e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}}}{x^2}+\frac {e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}}}{x}\right ) \, dx \\ & = \log (x)-134369280 \int \frac {e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}}}{x \left (-134369280+x \log ^4(x)\right )} \, dx+268738560 \int \frac {e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}}}{x^2 \left (-134369280+x \log ^4(x)\right )} \, dx+537477120 \int \frac {e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}} \log ^3(x)}{x \left (-134369280+x \log ^4(x)\right )^2} \, dx+18055103407718400 \int \frac {e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}}}{x^2 \left (-134369280+x \log ^4(x)\right )^2} \, dx+\int \frac {e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}}}{x^2} \, dx-\int \frac {e^{5+x+\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}}}{x} \, dx \\ \end{align*}
Time = 3.69 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.13 \[ \int \frac {18055103407718400-268738560 x \log ^4(x)+x^2 \log ^8(x)+e^{-\frac {e^{5+x} \log ^4(x)}{-134369280+x \log ^4(x)}} \left (537477120 e^{5+x} \log ^3(x)+134369280 e^{5+x} x \log ^4(x)+e^{5+x} \left (x-x^2\right ) \log ^8(x)\right )}{18055103407718400 x-268738560 x^2 \log ^4(x)+x^3 \log ^8(x)} \, dx=e^{\frac {e^{5+x} \log ^4(x)}{134369280-x \log ^4(x)}}+\log (x) \]
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Time = 1.08 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.09
\[\ln \left (x \right )+{\mathrm e}^{-\frac {{\mathrm e}^{5+x} \ln \left (x \right )^{4}}{x \ln \left (x \right )^{4}-134369280}}\]
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Time = 0.28 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.04 \[ \int \frac {18055103407718400-268738560 x \log ^4(x)+x^2 \log ^8(x)+e^{-\frac {e^{5+x} \log ^4(x)}{-134369280+x \log ^4(x)}} \left (537477120 e^{5+x} \log ^3(x)+134369280 e^{5+x} x \log ^4(x)+e^{5+x} \left (x-x^2\right ) \log ^8(x)\right )}{18055103407718400 x-268738560 x^2 \log ^4(x)+x^3 \log ^8(x)} \, dx=e^{\left (-\frac {e^{\left (x + 5\right )} \log \left (x\right )^{4}}{x \log \left (x\right )^{4} - 134369280}\right )} + \log \left (x\right ) \]
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Time = 0.52 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.04 \[ \int \frac {18055103407718400-268738560 x \log ^4(x)+x^2 \log ^8(x)+e^{-\frac {e^{5+x} \log ^4(x)}{-134369280+x \log ^4(x)}} \left (537477120 e^{5+x} \log ^3(x)+134369280 e^{5+x} x \log ^4(x)+e^{5+x} \left (x-x^2\right ) \log ^8(x)\right )}{18055103407718400 x-268738560 x^2 \log ^4(x)+x^3 \log ^8(x)} \, dx=\log {\left (x \right )} + e^{- \frac {e^{x + 5} \log {\left (x \right )}^{4}}{x \log {\left (x \right )}^{4} - 134369280}} \]
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Time = 0.25 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.04 \[ \int \frac {18055103407718400-268738560 x \log ^4(x)+x^2 \log ^8(x)+e^{-\frac {e^{5+x} \log ^4(x)}{-134369280+x \log ^4(x)}} \left (537477120 e^{5+x} \log ^3(x)+134369280 e^{5+x} x \log ^4(x)+e^{5+x} \left (x-x^2\right ) \log ^8(x)\right )}{18055103407718400 x-268738560 x^2 \log ^4(x)+x^3 \log ^8(x)} \, dx=e^{\left (-\frac {e^{\left (x + 5\right )} \log \left (x\right )^{4}}{x \log \left (x\right )^{4} - 134369280}\right )} + \log \left (x\right ) \]
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\[ \int \frac {18055103407718400-268738560 x \log ^4(x)+x^2 \log ^8(x)+e^{-\frac {e^{5+x} \log ^4(x)}{-134369280+x \log ^4(x)}} \left (537477120 e^{5+x} \log ^3(x)+134369280 e^{5+x} x \log ^4(x)+e^{5+x} \left (x-x^2\right ) \log ^8(x)\right )}{18055103407718400 x-268738560 x^2 \log ^4(x)+x^3 \log ^8(x)} \, dx=\int { \frac {x^{2} \log \left (x\right )^{8} - 268738560 \, x \log \left (x\right )^{4} - {\left ({\left (x^{2} - x\right )} e^{\left (x + 5\right )} \log \left (x\right )^{8} - 134369280 \, x e^{\left (x + 5\right )} \log \left (x\right )^{4} - 537477120 \, e^{\left (x + 5\right )} \log \left (x\right )^{3}\right )} e^{\left (-\frac {e^{\left (x + 5\right )} \log \left (x\right )^{4}}{x \log \left (x\right )^{4} - 134369280}\right )} + 18055103407718400}{x^{3} \log \left (x\right )^{8} - 268738560 \, x^{2} \log \left (x\right )^{4} + 18055103407718400 \, x} \,d x } \]
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Time = 8.74 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.04 \[ \int \frac {18055103407718400-268738560 x \log ^4(x)+x^2 \log ^8(x)+e^{-\frac {e^{5+x} \log ^4(x)}{-134369280+x \log ^4(x)}} \left (537477120 e^{5+x} \log ^3(x)+134369280 e^{5+x} x \log ^4(x)+e^{5+x} \left (x-x^2\right ) \log ^8(x)\right )}{18055103407718400 x-268738560 x^2 \log ^4(x)+x^3 \log ^8(x)} \, dx={\mathrm {e}}^{-\frac {{\mathrm {e}}^5\,{\mathrm {e}}^x\,{\ln \left (x\right )}^4}{x\,{\ln \left (x\right )}^4-134369280}}+\ln \left (x\right ) \]
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