Integrand size = 79, antiderivative size = 16 \[ \int \frac {\left (32 x^3-32 x^4 \log (x)\right ) \log (-4+x-\log (\log (x)))+\left (\left (256 x^3-64 x^4\right ) \log (x)+64 x^3 \log (x) \log (\log (x))\right ) \log ^2(-4+x-\log (\log (x)))}{(4-x) \log (x)+\log (x) \log (\log (x))} \, dx=16 x^4 \log ^2(-4+x-\log (\log (x))) \]
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\[ \int \frac {\left (32 x^3-32 x^4 \log (x)\right ) \log (-4+x-\log (\log (x)))+\left (\left (256 x^3-64 x^4\right ) \log (x)+64 x^3 \log (x) \log (\log (x))\right ) \log ^2(-4+x-\log (\log (x)))}{(4-x) \log (x)+\log (x) \log (\log (x))} \, dx=\int \frac {\left (32 x^3-32 x^4 \log (x)\right ) \log (-4+x-\log (\log (x)))+\left (\left (256 x^3-64 x^4\right ) \log (x)+64 x^3 \log (x) \log (\log (x))\right ) \log ^2(-4+x-\log (\log (x)))}{(4-x) \log (x)+\log (x) \log (\log (x))} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {32 x^3 \log (-4+x-\log (\log (x))) (1-\log (x) (x+2 (-4+x-\log (\log (x))) \log (-4+x-\log (\log (x)))))}{\log (x) (4-x+\log (\log (x)))} \, dx \\ & = 32 \int \frac {x^3 \log (-4+x-\log (\log (x))) (1-\log (x) (x+2 (-4+x-\log (\log (x))) \log (-4+x-\log (\log (x)))))}{\log (x) (4-x+\log (\log (x)))} \, dx \\ & = 32 \int \left (\frac {x^3 (-1+x \log (x)) \log (-4+x-\log (\log (x)))}{\log (x) (-4+x-\log (\log (x)))}+2 x^3 \log ^2(-4+x-\log (\log (x)))\right ) \, dx \\ & = 32 \int \frac {x^3 (-1+x \log (x)) \log (-4+x-\log (\log (x)))}{\log (x) (-4+x-\log (\log (x)))} \, dx+64 \int x^3 \log ^2(-4+x-\log (\log (x))) \, dx \\ & = 32 \int \left (\frac {x^4 \log (-4+x-\log (\log (x)))}{-4+x-\log (\log (x))}-\frac {x^3 \log (-4+x-\log (\log (x)))}{\log (x) (-4+x-\log (\log (x)))}\right ) \, dx+64 \int x^3 \log ^2(-4+x-\log (\log (x))) \, dx \\ & = 32 \int \frac {x^4 \log (-4+x-\log (\log (x)))}{-4+x-\log (\log (x))} \, dx-32 \int \frac {x^3 \log (-4+x-\log (\log (x)))}{\log (x) (-4+x-\log (\log (x)))} \, dx+64 \int x^3 \log ^2(-4+x-\log (\log (x))) \, dx \\ \end{align*}
\[ \int \frac {\left (32 x^3-32 x^4 \log (x)\right ) \log (-4+x-\log (\log (x)))+\left (\left (256 x^3-64 x^4\right ) \log (x)+64 x^3 \log (x) \log (\log (x))\right ) \log ^2(-4+x-\log (\log (x)))}{(4-x) \log (x)+\log (x) \log (\log (x))} \, dx=\int \frac {\left (32 x^3-32 x^4 \log (x)\right ) \log (-4+x-\log (\log (x)))+\left (\left (256 x^3-64 x^4\right ) \log (x)+64 x^3 \log (x) \log (\log (x))\right ) \log ^2(-4+x-\log (\log (x)))}{(4-x) \log (x)+\log (x) \log (\log (x))} \, dx \]
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Time = 2.88 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.06
method | result | size |
risch | \(16 x^{4} \ln \left (-\ln \left (\ln \left (x \right )\right )+x -4\right )^{2}\) | \(17\) |
parallelrisch | \(16 x^{4} \ln \left (-\ln \left (\ln \left (x \right )\right )+x -4\right )^{2}\) | \(17\) |
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Time = 0.24 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00 \[ \int \frac {\left (32 x^3-32 x^4 \log (x)\right ) \log (-4+x-\log (\log (x)))+\left (\left (256 x^3-64 x^4\right ) \log (x)+64 x^3 \log (x) \log (\log (x))\right ) \log ^2(-4+x-\log (\log (x)))}{(4-x) \log (x)+\log (x) \log (\log (x))} \, dx=16 \, x^{4} \log \left (x - \log \left (\log \left (x\right )\right ) - 4\right )^{2} \]
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Time = 0.44 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94 \[ \int \frac {\left (32 x^3-32 x^4 \log (x)\right ) \log (-4+x-\log (\log (x)))+\left (\left (256 x^3-64 x^4\right ) \log (x)+64 x^3 \log (x) \log (\log (x))\right ) \log ^2(-4+x-\log (\log (x)))}{(4-x) \log (x)+\log (x) \log (\log (x))} \, dx=16 x^{4} \log {\left (x - \log {\left (\log {\left (x \right )} \right )} - 4 \right )}^{2} \]
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Time = 0.23 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00 \[ \int \frac {\left (32 x^3-32 x^4 \log (x)\right ) \log (-4+x-\log (\log (x)))+\left (\left (256 x^3-64 x^4\right ) \log (x)+64 x^3 \log (x) \log (\log (x))\right ) \log ^2(-4+x-\log (\log (x)))}{(4-x) \log (x)+\log (x) \log (\log (x))} \, dx=16 \, x^{4} \log \left (x - \log \left (\log \left (x\right )\right ) - 4\right )^{2} \]
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Time = 0.38 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00 \[ \int \frac {\left (32 x^3-32 x^4 \log (x)\right ) \log (-4+x-\log (\log (x)))+\left (\left (256 x^3-64 x^4\right ) \log (x)+64 x^3 \log (x) \log (\log (x))\right ) \log ^2(-4+x-\log (\log (x)))}{(4-x) \log (x)+\log (x) \log (\log (x))} \, dx=16 \, x^{4} \log \left (x - \log \left (\log \left (x\right )\right ) - 4\right )^{2} \]
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Time = 14.22 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00 \[ \int \frac {\left (32 x^3-32 x^4 \log (x)\right ) \log (-4+x-\log (\log (x)))+\left (\left (256 x^3-64 x^4\right ) \log (x)+64 x^3 \log (x) \log (\log (x))\right ) \log ^2(-4+x-\log (\log (x)))}{(4-x) \log (x)+\log (x) \log (\log (x))} \, dx=16\,x^4\,{\ln \left (x-\ln \left (\ln \left (x\right )\right )-4\right )}^2 \]
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