Integrand size = 124, antiderivative size = 20 \[ \int \frac {-90 x^2-18 x^3-2 x^4-2 x^3 \log (x)+\left (-10 x^2+18 x^3+4 x^4+\left (30 x^2+6 x^3\right ) \log (x)\right ) \log (5+x)}{45+9 x+\left (-30 x-6 x^2+(-30-6 x) \log (x)\right ) \log (5+x)+\left (5 x^2+x^3+\left (10 x+2 x^2\right ) \log (x)+(5+x) \log ^2(x)\right ) \log ^2(5+x)} \, dx=27+\frac {2 x^3}{-3+(x+\log (x)) \log (5+x)} \]
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\[ \int \frac {-90 x^2-18 x^3-2 x^4-2 x^3 \log (x)+\left (-10 x^2+18 x^3+4 x^4+\left (30 x^2+6 x^3\right ) \log (x)\right ) \log (5+x)}{45+9 x+\left (-30 x-6 x^2+(-30-6 x) \log (x)\right ) \log (5+x)+\left (5 x^2+x^3+\left (10 x+2 x^2\right ) \log (x)+(5+x) \log ^2(x)\right ) \log ^2(5+x)} \, dx=\int \frac {-90 x^2-18 x^3-2 x^4-2 x^3 \log (x)+\left (-10 x^2+18 x^3+4 x^4+\left (30 x^2+6 x^3\right ) \log (x)\right ) \log (5+x)}{45+9 x+\left (-30 x-6 x^2+(-30-6 x) \log (x)\right ) \log (5+x)+\left (5 x^2+x^3+\left (10 x+2 x^2\right ) \log (x)+(5+x) \log ^2(x)\right ) \log ^2(5+x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {2 x^2 \left (-45-9 x-x^2+\left (-5+9 x+2 x^2\right ) \log (5+x)+\log (x) (-x+3 (5+x) \log (5+x))\right )}{(5+x) (3-(x+\log (x)) \log (5+x))^2} \, dx \\ & = 2 \int \frac {x^2 \left (-45-9 x-x^2+\left (-5+9 x+2 x^2\right ) \log (5+x)+\log (x) (-x+3 (5+x) \log (5+x))\right )}{(5+x) (3-(x+\log (x)) \log (5+x))^2} \, dx \\ & = 2 \int \left (-\frac {x^2 \left (15+18 x+3 x^2+x^3+2 x^2 \log (x)+x \log ^2(x)\right )}{(5+x) (x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}+\frac {x^2 (-1+2 x+3 \log (x))}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))}\right ) \, dx \\ & = -\left (2 \int \frac {x^2 \left (15+18 x+3 x^2+x^3+2 x^2 \log (x)+x \log ^2(x)\right )}{(5+x) (x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx\right )+2 \int \frac {x^2 (-1+2 x+3 \log (x))}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))} \, dx \\ & = -\left (2 \int \left (-\frac {5 \left (15+18 x+3 x^2+x^3+2 x^2 \log (x)+x \log ^2(x)\right )}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}+\frac {x \left (15+18 x+3 x^2+x^3+2 x^2 \log (x)+x \log ^2(x)\right )}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}+\frac {25 \left (15+18 x+3 x^2+x^3+2 x^2 \log (x)+x \log ^2(x)\right )}{(5+x) (x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}\right ) \, dx\right )+2 \int \left (-\frac {x^2}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))}+\frac {2 x^3}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))}+\frac {3 x^2 \log (x)}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))}\right ) \, dx \\ & = -\left (2 \int \frac {x \left (15+18 x+3 x^2+x^3+2 x^2 \log (x)+x \log ^2(x)\right )}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx\right )-2 \int \frac {x^2}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))} \, dx+4 \int \frac {x^3}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))} \, dx+6 \int \frac {x^2 \log (x)}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))} \, dx+10 \int \frac {15+18 x+3 x^2+x^3+2 x^2 \log (x)+x \log ^2(x)}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx-50 \int \frac {15+18 x+3 x^2+x^3+2 x^2 \log (x)+x \log ^2(x)}{(5+x) (x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx \\ & = -\left (2 \int \frac {x^2}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))} \, dx\right )-2 \int \left (\frac {15 x}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}+\frac {18 x^2}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}+\frac {3 x^3}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}+\frac {x^4}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}+\frac {2 x^3 \log (x)}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}+\frac {x^2 \log ^2(x)}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}\right ) \, dx+4 \int \frac {x^3}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))} \, dx+6 \int \frac {x^2 \log (x)}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))} \, dx+10 \int \left (\frac {15}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}+\frac {18 x}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}+\frac {3 x^2}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}+\frac {x^3}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}+\frac {2 x^2 \log (x)}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}+\frac {x \log ^2(x)}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}\right ) \, dx-50 \int \left (\frac {15}{(5+x) (x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}+\frac {18 x}{(5+x) (x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}+\frac {3 x^2}{(5+x) (x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}+\frac {x^3}{(5+x) (x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}+\frac {2 x^2 \log (x)}{(5+x) (x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}+\frac {x \log ^2(x)}{(5+x) (x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}\right ) \, dx \\ & = -\left (2 \int \frac {x^4}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx\right )-2 \int \frac {x^2 \log ^2(x)}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx-2 \int \frac {x^2}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))} \, dx-4 \int \frac {x^3 \log (x)}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx+4 \int \frac {x^3}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))} \, dx-6 \int \frac {x^3}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx+6 \int \frac {x^2 \log (x)}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))} \, dx+10 \int \frac {x^3}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx+10 \int \frac {x \log ^2(x)}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx+20 \int \frac {x^2 \log (x)}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx-30 \int \frac {x}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx+30 \int \frac {x^2}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx-36 \int \frac {x^2}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx-50 \int \frac {x^3}{(5+x) (x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx-50 \int \frac {x \log ^2(x)}{(5+x) (x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx-100 \int \frac {x^2 \log (x)}{(5+x) (x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx+150 \int \frac {1}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx-150 \int \frac {x^2}{(5+x) (x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx+180 \int \frac {x}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx-750 \int \frac {1}{(5+x) (x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx-900 \int \frac {x}{(5+x) (x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx \\ & = -\left (2 \int \frac {x^4}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx\right )-2 \int \frac {x^2 \log ^2(x)}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx-2 \int \frac {x^2}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))} \, dx-4 \int \frac {x^3 \log (x)}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx+4 \int \frac {x^3}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))} \, dx-6 \int \frac {x^3}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx+6 \int \frac {x^2 \log (x)}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))} \, dx+10 \int \frac {x^3}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx+10 \int \frac {x \log ^2(x)}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx+20 \int \frac {x^2 \log (x)}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx-30 \int \frac {x}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx+30 \int \frac {x^2}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx-36 \int \frac {x^2}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx-50 \int \left (\frac {25}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}-\frac {5 x}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}+\frac {x^2}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}-\frac {125}{(5+x) (x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}\right ) \, dx-50 \int \left (\frac {\log ^2(x)}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}-\frac {5 \log ^2(x)}{(5+x) (x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}\right ) \, dx-100 \int \left (-\frac {5 \log (x)}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}+\frac {x \log (x)}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}+\frac {25 \log (x)}{(5+x) (x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}\right ) \, dx+150 \int \frac {1}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx-150 \int \left (-\frac {5}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}+\frac {x}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}+\frac {25}{(5+x) (x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}\right ) \, dx+180 \int \frac {x}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx-750 \int \frac {1}{(5+x) (x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx-900 \int \left (\frac {1}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}-\frac {5}{(5+x) (x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2}\right ) \, dx \\ & = -\left (2 \int \frac {x^4}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx\right )-2 \int \frac {x^2 \log ^2(x)}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx-2 \int \frac {x^2}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))} \, dx-4 \int \frac {x^3 \log (x)}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx+4 \int \frac {x^3}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))} \, dx-6 \int \frac {x^3}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx+6 \int \frac {x^2 \log (x)}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))} \, dx+10 \int \frac {x^3}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx+10 \int \frac {x \log ^2(x)}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx+20 \int \frac {x^2 \log (x)}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx-30 \int \frac {x}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx+30 \int \frac {x^2}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx-36 \int \frac {x^2}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx-50 \int \frac {x^2}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx-50 \int \frac {\log ^2(x)}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx-100 \int \frac {x \log (x)}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx+150 \int \frac {1}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx-150 \int \frac {x}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx+180 \int \frac {x}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx+250 \int \frac {x}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx+250 \int \frac {\log ^2(x)}{(5+x) (x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx+500 \int \frac {\log (x)}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx+750 \int \frac {1}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx-750 \int \frac {1}{(5+x) (x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx-900 \int \frac {1}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx-1250 \int \frac {1}{(x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx-2500 \int \frac {\log (x)}{(5+x) (x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx-3750 \int \frac {1}{(5+x) (x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx+4500 \int \frac {1}{(5+x) (x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx+6250 \int \frac {1}{(5+x) (x+\log (x)) (-3+x \log (5+x)+\log (x) \log (5+x))^2} \, dx \\ \end{align*}
Time = 0.65 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.90 \[ \int \frac {-90 x^2-18 x^3-2 x^4-2 x^3 \log (x)+\left (-10 x^2+18 x^3+4 x^4+\left (30 x^2+6 x^3\right ) \log (x)\right ) \log (5+x)}{45+9 x+\left (-30 x-6 x^2+(-30-6 x) \log (x)\right ) \log (5+x)+\left (5 x^2+x^3+\left (10 x+2 x^2\right ) \log (x)+(5+x) \log ^2(x)\right ) \log ^2(5+x)} \, dx=\frac {2 x^3}{-3+(x+\log (x)) \log (5+x)} \]
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Time = 1.29 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.15
method | result | size |
default | \(\frac {2 x^{3}}{\ln \left (x \right ) \ln \left (5+x \right )+x \ln \left (5+x \right )-3}\) | \(23\) |
risch | \(\frac {2 x^{3}}{\ln \left (x \right ) \ln \left (5+x \right )+x \ln \left (5+x \right )-3}\) | \(23\) |
parallelrisch | \(\frac {2 x^{3}}{\ln \left (x \right ) \ln \left (5+x \right )+x \ln \left (5+x \right )-3}\) | \(23\) |
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Time = 0.24 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.90 \[ \int \frac {-90 x^2-18 x^3-2 x^4-2 x^3 \log (x)+\left (-10 x^2+18 x^3+4 x^4+\left (30 x^2+6 x^3\right ) \log (x)\right ) \log (5+x)}{45+9 x+\left (-30 x-6 x^2+(-30-6 x) \log (x)\right ) \log (5+x)+\left (5 x^2+x^3+\left (10 x+2 x^2\right ) \log (x)+(5+x) \log ^2(x)\right ) \log ^2(5+x)} \, dx=\frac {2 \, x^{3}}{{\left (x + \log \left (x\right )\right )} \log \left (x + 5\right ) - 3} \]
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Time = 0.14 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.75 \[ \int \frac {-90 x^2-18 x^3-2 x^4-2 x^3 \log (x)+\left (-10 x^2+18 x^3+4 x^4+\left (30 x^2+6 x^3\right ) \log (x)\right ) \log (5+x)}{45+9 x+\left (-30 x-6 x^2+(-30-6 x) \log (x)\right ) \log (5+x)+\left (5 x^2+x^3+\left (10 x+2 x^2\right ) \log (x)+(5+x) \log ^2(x)\right ) \log ^2(5+x)} \, dx=\frac {2 x^{3}}{\left (x + \log {\left (x \right )}\right ) \log {\left (x + 5 \right )} - 3} \]
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Time = 0.26 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.90 \[ \int \frac {-90 x^2-18 x^3-2 x^4-2 x^3 \log (x)+\left (-10 x^2+18 x^3+4 x^4+\left (30 x^2+6 x^3\right ) \log (x)\right ) \log (5+x)}{45+9 x+\left (-30 x-6 x^2+(-30-6 x) \log (x)\right ) \log (5+x)+\left (5 x^2+x^3+\left (10 x+2 x^2\right ) \log (x)+(5+x) \log ^2(x)\right ) \log ^2(5+x)} \, dx=\frac {2 \, x^{3}}{{\left (x + \log \left (x\right )\right )} \log \left (x + 5\right ) - 3} \]
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Time = 0.30 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {-90 x^2-18 x^3-2 x^4-2 x^3 \log (x)+\left (-10 x^2+18 x^3+4 x^4+\left (30 x^2+6 x^3\right ) \log (x)\right ) \log (5+x)}{45+9 x+\left (-30 x-6 x^2+(-30-6 x) \log (x)\right ) \log (5+x)+\left (5 x^2+x^3+\left (10 x+2 x^2\right ) \log (x)+(5+x) \log ^2(x)\right ) \log ^2(5+x)} \, dx=\frac {2 \, x^{3}}{x \log \left (x + 5\right ) + \log \left (x + 5\right ) \log \left (x\right ) - 3} \]
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Timed out. \[ \int \frac {-90 x^2-18 x^3-2 x^4-2 x^3 \log (x)+\left (-10 x^2+18 x^3+4 x^4+\left (30 x^2+6 x^3\right ) \log (x)\right ) \log (5+x)}{45+9 x+\left (-30 x-6 x^2+(-30-6 x) \log (x)\right ) \log (5+x)+\left (5 x^2+x^3+\left (10 x+2 x^2\right ) \log (x)+(5+x) \log ^2(x)\right ) \log ^2(5+x)} \, dx=\int -\frac {2\,x^3\,\ln \left (x\right )-\ln \left (x+5\right )\,\left (\ln \left (x\right )\,\left (6\,x^3+30\,x^2\right )-10\,x^2+18\,x^3+4\,x^4\right )+90\,x^2+18\,x^3+2\,x^4}{\left ({\ln \left (x\right )}^2\,\left (x+5\right )+\ln \left (x\right )\,\left (2\,x^2+10\,x\right )+5\,x^2+x^3\right )\,{\ln \left (x+5\right )}^2+\left (-30\,x-\ln \left (x\right )\,\left (6\,x+30\right )-6\,x^2\right )\,\ln \left (x+5\right )+9\,x+45} \,d x \]
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