Integrand size = 208, antiderivative size = 37 \[ \int \frac {-24 e^5 x^4+\left (432-108 x-108 x^2+27 x^3+e^{10} \left (-32 x^3+8 x^4\right )\right ) \log (4-x)+\left (72 x^4+e^5 \left (192 x^3-48 x^4\right ) \log (4-x)\right ) \log (\log (4-x))+\left (-288 x^3+72 x^4\right ) \log (4-x) \log ^2(\log (4-x))}{\left (-432 x+108 x^2-108 x^3+27 x^4+e^{10} \left (-16 x^4+4 x^5\right )\right ) \log (4-x)+e^5 \left (96 x^4-24 x^5\right ) \log (4-x) \log (\log (4-x))+\left (-144 x^4+36 x^5\right ) \log (4-x) \log ^2(\log (4-x))} \, dx=\log \left (5 \left (-x+4 \left (\frac {3}{x}+x+x^2 \left (-\frac {e^5}{3}+\log (\log (4-x))\right )^2\right )\right )\right ) \]
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\[ \int \frac {-24 e^5 x^4+\left (432-108 x-108 x^2+27 x^3+e^{10} \left (-32 x^3+8 x^4\right )\right ) \log (4-x)+\left (72 x^4+e^5 \left (192 x^3-48 x^4\right ) \log (4-x)\right ) \log (\log (4-x))+\left (-288 x^3+72 x^4\right ) \log (4-x) \log ^2(\log (4-x))}{\left (-432 x+108 x^2-108 x^3+27 x^4+e^{10} \left (-16 x^4+4 x^5\right )\right ) \log (4-x)+e^5 \left (96 x^4-24 x^5\right ) \log (4-x) \log (\log (4-x))+\left (-144 x^4+36 x^5\right ) \log (4-x) \log ^2(\log (4-x))} \, dx=\int \frac {-24 e^5 x^4+\left (432-108 x-108 x^2+27 x^3+e^{10} \left (-32 x^3+8 x^4\right )\right ) \log (4-x)+\left (72 x^4+e^5 \left (192 x^3-48 x^4\right ) \log (4-x)\right ) \log (\log (4-x))+\left (-288 x^3+72 x^4\right ) \log (4-x) \log ^2(\log (4-x))}{\left (-432 x+108 x^2-108 x^3+27 x^4+e^{10} \left (-16 x^4+4 x^5\right )\right ) \log (4-x)+e^5 \left (96 x^4-24 x^5\right ) \log (4-x) \log (\log (4-x))+\left (-144 x^4+36 x^5\right ) \log (4-x) \log ^2(\log (4-x))} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {24 x^4 \left (e^5-3 \log (\log (4-x))\right )-(-4+x) \log (4-x) \left (-108+27 x^2+8 e^{10} x^3-48 e^5 x^3 \log (\log (4-x))+72 x^3 \log ^2(\log (4-x))\right )}{(4-x) x \log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )} \, dx \\ & = \int \left (\frac {2}{x}-\frac {3 \left (8 e^5 x^4-432 \log (4-x)+108 x \log (4-x)-36 x^2 \log (4-x)+9 x^3 \log (4-x)-24 x^4 \log (\log (4-x))\right )}{(-4+x) x \log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )}\right ) \, dx \\ & = 2 \log (x)-3 \int \frac {8 e^5 x^4-432 \log (4-x)+108 x \log (4-x)-36 x^2 \log (4-x)+9 x^3 \log (4-x)-24 x^4 \log (\log (4-x))}{(-4+x) x \log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )} \, dx \\ & = 2 \log (x)-3 \int \frac {-9 \left (-48+12 x-4 x^2+x^3\right ) \log (4-x)-8 x^4 \left (e^5-3 \log (\log (4-x))\right )}{(4-x) x \log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )} \, dx \\ & = 2 \log (x)-3 \int \left (\frac {8 e^5 x^4-432 \log (4-x)+108 x \log (4-x)-36 x^2 \log (4-x)+9 x^3 \log (4-x)-24 x^4 \log (\log (4-x))}{4 (-4+x) \log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )}+\frac {-8 e^5 x^4+432 \log (4-x)-108 x \log (4-x)+36 x^2 \log (4-x)-9 x^3 \log (4-x)+24 x^4 \log (\log (4-x))}{4 x \log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )}\right ) \, dx \\ & = 2 \log (x)-\frac {3}{4} \int \frac {8 e^5 x^4-432 \log (4-x)+108 x \log (4-x)-36 x^2 \log (4-x)+9 x^3 \log (4-x)-24 x^4 \log (\log (4-x))}{(-4+x) \log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )} \, dx-\frac {3}{4} \int \frac {-8 e^5 x^4+432 \log (4-x)-108 x \log (4-x)+36 x^2 \log (4-x)-9 x^3 \log (4-x)+24 x^4 \log (\log (4-x))}{x \log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )} \, dx \\ & = 2 \log (x)-\frac {3}{4} \int \frac {-9 \left (-48+12 x-4 x^2+x^3\right ) \log (4-x)-8 x^4 \left (e^5-3 \log (\log (4-x))\right )}{(4-x) \log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )} \, dx-\frac {3}{4} \int \frac {-9 \left (-48+12 x-4 x^2+x^3\right ) \log (4-x)-8 x^4 \left (e^5-3 \log (\log (4-x))\right )}{x \log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )} \, dx \\ & = 2 \log (x)-\frac {3}{4} \int \left (-\frac {108}{108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))}+\frac {432}{x \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )}+\frac {36 x}{108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))}-\frac {9 x^2}{108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))}-\frac {8 e^5 x^3}{\log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )}+\frac {24 x^3 \log (\log (4-x))}{\log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )}\right ) \, dx-\frac {3}{4} \int \left (-\frac {432}{(-4+x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )}+\frac {108 x}{(-4+x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )}-\frac {36 x^2}{(-4+x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )}+\frac {9 x^3}{(-4+x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )}+\frac {8 e^5 x^4}{(-4+x) \log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )}-\frac {24 x^4 \log (\log (4-x))}{(-4+x) \log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )}\right ) \, dx \\ & = 2 \log (x)+\frac {27}{4} \int \frac {x^2}{108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))} \, dx-\frac {27}{4} \int \frac {x^3}{(-4+x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )} \, dx-18 \int \frac {x^3 \log (\log (4-x))}{\log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )} \, dx+18 \int \frac {x^4 \log (\log (4-x))}{(-4+x) \log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )} \, dx-27 \int \frac {x}{108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))} \, dx+27 \int \frac {x^2}{(-4+x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )} \, dx+81 \int \frac {1}{108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))} \, dx-81 \int \frac {x}{(-4+x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )} \, dx+324 \int \frac {1}{(-4+x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )} \, dx-324 \int \frac {1}{x \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )} \, dx+\left (6 e^5\right ) \int \frac {x^3}{\log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )} \, dx-\left (6 e^5\right ) \int \frac {x^4}{(-4+x) \log (4-x) \left (108+27 x^2+4 e^{10} x^3-24 e^5 x^3 \log (\log (4-x))+36 x^3 \log ^2(\log (4-x))\right )} \, dx \\ & = \text {Too large to display} \\ \end{align*}
\[ \int \frac {-24 e^5 x^4+\left (432-108 x-108 x^2+27 x^3+e^{10} \left (-32 x^3+8 x^4\right )\right ) \log (4-x)+\left (72 x^4+e^5 \left (192 x^3-48 x^4\right ) \log (4-x)\right ) \log (\log (4-x))+\left (-288 x^3+72 x^4\right ) \log (4-x) \log ^2(\log (4-x))}{\left (-432 x+108 x^2-108 x^3+27 x^4+e^{10} \left (-16 x^4+4 x^5\right )\right ) \log (4-x)+e^5 \left (96 x^4-24 x^5\right ) \log (4-x) \log (\log (4-x))+\left (-144 x^4+36 x^5\right ) \log (4-x) \log ^2(\log (4-x))} \, dx=\int \frac {-24 e^5 x^4+\left (432-108 x-108 x^2+27 x^3+e^{10} \left (-32 x^3+8 x^4\right )\right ) \log (4-x)+\left (72 x^4+e^5 \left (192 x^3-48 x^4\right ) \log (4-x)\right ) \log (\log (4-x))+\left (-288 x^3+72 x^4\right ) \log (4-x) \log ^2(\log (4-x))}{\left (-432 x+108 x^2-108 x^3+27 x^4+e^{10} \left (-16 x^4+4 x^5\right )\right ) \log (4-x)+e^5 \left (96 x^4-24 x^5\right ) \log (4-x) \log (\log (4-x))+\left (-144 x^4+36 x^5\right ) \log (4-x) \log ^2(\log (4-x))} \, dx \]
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Time = 4.99 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.27
method | result | size |
risch | \(2 \ln \left (x \right )+\ln \left (\ln \left (\ln \left (-x +4\right )\right )^{2}-\frac {2 \,{\mathrm e}^{5} \ln \left (\ln \left (-x +4\right )\right )}{3}+\frac {4 x^{3} {\mathrm e}^{10}+27 x^{2}+108}{36 x^{3}}\right )\) | \(47\) |
parallelrisch | \(-\ln \left (x \right )+\ln \left (\frac {x^{3} {\mathrm e}^{10}}{9}-\frac {2 \,{\mathrm e}^{5} \ln \left (\ln \left (-x +4\right )\right ) x^{3}}{3}+\ln \left (\ln \left (-x +4\right )\right )^{2} x^{3}+\frac {3 x^{2}}{4}+3\right )\) | \(50\) |
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Time = 0.27 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.43 \[ \int \frac {-24 e^5 x^4+\left (432-108 x-108 x^2+27 x^3+e^{10} \left (-32 x^3+8 x^4\right )\right ) \log (4-x)+\left (72 x^4+e^5 \left (192 x^3-48 x^4\right ) \log (4-x)\right ) \log (\log (4-x))+\left (-288 x^3+72 x^4\right ) \log (4-x) \log ^2(\log (4-x))}{\left (-432 x+108 x^2-108 x^3+27 x^4+e^{10} \left (-16 x^4+4 x^5\right )\right ) \log (4-x)+e^5 \left (96 x^4-24 x^5\right ) \log (4-x) \log (\log (4-x))+\left (-144 x^4+36 x^5\right ) \log (4-x) \log ^2(\log (4-x))} \, dx=2 \, \log \left (x\right ) + \log \left (-\frac {24 \, x^{3} e^{5} \log \left (\log \left (-x + 4\right )\right ) - 36 \, x^{3} \log \left (\log \left (-x + 4\right )\right )^{2} - 4 \, x^{3} e^{10} - 27 \, x^{2} - 108}{x^{3}}\right ) \]
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Time = 0.40 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.30 \[ \int \frac {-24 e^5 x^4+\left (432-108 x-108 x^2+27 x^3+e^{10} \left (-32 x^3+8 x^4\right )\right ) \log (4-x)+\left (72 x^4+e^5 \left (192 x^3-48 x^4\right ) \log (4-x)\right ) \log (\log (4-x))+\left (-288 x^3+72 x^4\right ) \log (4-x) \log ^2(\log (4-x))}{\left (-432 x+108 x^2-108 x^3+27 x^4+e^{10} \left (-16 x^4+4 x^5\right )\right ) \log (4-x)+e^5 \left (96 x^4-24 x^5\right ) \log (4-x) \log (\log (4-x))+\left (-144 x^4+36 x^5\right ) \log (4-x) \log ^2(\log (4-x))} \, dx=2 \log {\left (x \right )} + \log {\left (\log {\left (\log {\left (4 - x \right )} \right )}^{2} - \frac {2 e^{5} \log {\left (\log {\left (4 - x \right )} \right )}}{3} + \frac {4 x^{3} e^{10} + 27 x^{2} + 108}{36 x^{3}} \right )} \]
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Time = 0.25 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.43 \[ \int \frac {-24 e^5 x^4+\left (432-108 x-108 x^2+27 x^3+e^{10} \left (-32 x^3+8 x^4\right )\right ) \log (4-x)+\left (72 x^4+e^5 \left (192 x^3-48 x^4\right ) \log (4-x)\right ) \log (\log (4-x))+\left (-288 x^3+72 x^4\right ) \log (4-x) \log ^2(\log (4-x))}{\left (-432 x+108 x^2-108 x^3+27 x^4+e^{10} \left (-16 x^4+4 x^5\right )\right ) \log (4-x)+e^5 \left (96 x^4-24 x^5\right ) \log (4-x) \log (\log (4-x))+\left (-144 x^4+36 x^5\right ) \log (4-x) \log ^2(\log (4-x))} \, dx=2 \, \log \left (x\right ) + \log \left (-\frac {24 \, x^{3} e^{5} \log \left (\log \left (-x + 4\right )\right ) - 36 \, x^{3} \log \left (\log \left (-x + 4\right )\right )^{2} - 4 \, x^{3} e^{10} - 27 \, x^{2} - 108}{36 \, x^{3}}\right ) \]
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Time = 0.45 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.30 \[ \int \frac {-24 e^5 x^4+\left (432-108 x-108 x^2+27 x^3+e^{10} \left (-32 x^3+8 x^4\right )\right ) \log (4-x)+\left (72 x^4+e^5 \left (192 x^3-48 x^4\right ) \log (4-x)\right ) \log (\log (4-x))+\left (-288 x^3+72 x^4\right ) \log (4-x) \log ^2(\log (4-x))}{\left (-432 x+108 x^2-108 x^3+27 x^4+e^{10} \left (-16 x^4+4 x^5\right )\right ) \log (4-x)+e^5 \left (96 x^4-24 x^5\right ) \log (4-x) \log (\log (4-x))+\left (-144 x^4+36 x^5\right ) \log (4-x) \log ^2(\log (4-x))} \, dx=\log \left (-24 \, x^{3} e^{5} \log \left (\log \left (-x + 4\right )\right ) + 36 \, x^{3} \log \left (\log \left (-x + 4\right )\right )^{2} + 4 \, x^{3} e^{10} + 27 \, x^{2} + 108\right ) - \log \left (x\right ) \]
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Timed out. \[ \int \frac {-24 e^5 x^4+\left (432-108 x-108 x^2+27 x^3+e^{10} \left (-32 x^3+8 x^4\right )\right ) \log (4-x)+\left (72 x^4+e^5 \left (192 x^3-48 x^4\right ) \log (4-x)\right ) \log (\log (4-x))+\left (-288 x^3+72 x^4\right ) \log (4-x) \log ^2(\log (4-x))}{\left (-432 x+108 x^2-108 x^3+27 x^4+e^{10} \left (-16 x^4+4 x^5\right )\right ) \log (4-x)+e^5 \left (96 x^4-24 x^5\right ) \log (4-x) \log (\log (4-x))+\left (-144 x^4+36 x^5\right ) \log (4-x) \log ^2(\log (4-x))} \, dx=\int \frac {\ln \left (4-x\right )\,\left (108\,x+{\mathrm {e}}^{10}\,\left (32\,x^3-8\,x^4\right )+108\,x^2-27\,x^3-432\right )-\ln \left (\ln \left (4-x\right )\right )\,\left (72\,x^4+{\mathrm {e}}^5\,\ln \left (4-x\right )\,\left (192\,x^3-48\,x^4\right )\right )+24\,x^4\,{\mathrm {e}}^5+{\ln \left (\ln \left (4-x\right )\right )}^2\,\ln \left (4-x\right )\,\left (288\,x^3-72\,x^4\right )}{\ln \left (4-x\right )\,\left (144\,x^4-36\,x^5\right )\,{\ln \left (\ln \left (4-x\right )\right )}^2-{\mathrm {e}}^5\,\ln \left (4-x\right )\,\left (96\,x^4-24\,x^5\right )\,\ln \left (\ln \left (4-x\right )\right )+\ln \left (4-x\right )\,\left (432\,x+{\mathrm {e}}^{10}\,\left (16\,x^4-4\,x^5\right )-108\,x^2+108\,x^3-27\,x^4\right )} \,d x \]
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