Integrand size = 170, antiderivative size = 28 \[ \int \frac {e^4 \left (-1+17 x-4 x^2-12 x^3+3 x^4\right )+e^4 \left (4 x-3 x^3\right ) \log (x)+\left (e^4 \left (20-5 x-12 x^2+3 x^3\right )+e^4 \left (5-3 x^2\right ) \log (x)\right ) \log (-4+x-\log (x))+\left (e^4 \left (-4 x+x^2\right )-e^4 x \log (x)+\left (e^4 (-4+x)-e^4 \log (x)\right ) \log (-4+x-\log (x))\right ) \log (x+\log (-4+x-\log (x)))}{4 x-x^2+x \log (x)+(4-x+\log (x)) \log (-4+x-\log (x))} \, dx=e^4 \left (9+x \left (5-x^2-\log (x+\log (-4+x-\log (x)))\right )\right ) \]
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\[ \int \frac {e^4 \left (-1+17 x-4 x^2-12 x^3+3 x^4\right )+e^4 \left (4 x-3 x^3\right ) \log (x)+\left (e^4 \left (20-5 x-12 x^2+3 x^3\right )+e^4 \left (5-3 x^2\right ) \log (x)\right ) \log (-4+x-\log (x))+\left (e^4 \left (-4 x+x^2\right )-e^4 x \log (x)+\left (e^4 (-4+x)-e^4 \log (x)\right ) \log (-4+x-\log (x))\right ) \log (x+\log (-4+x-\log (x)))}{4 x-x^2+x \log (x)+(4-x+\log (x)) \log (-4+x-\log (x))} \, dx=\int \frac {e^4 \left (-1+17 x-4 x^2-12 x^3+3 x^4\right )+e^4 \left (4 x-3 x^3\right ) \log (x)+\left (e^4 \left (20-5 x-12 x^2+3 x^3\right )+e^4 \left (5-3 x^2\right ) \log (x)\right ) \log (-4+x-\log (x))+\left (e^4 \left (-4 x+x^2\right )-e^4 x \log (x)+\left (e^4 (-4+x)-e^4 \log (x)\right ) \log (-4+x-\log (x))\right ) \log (x+\log (-4+x-\log (x)))}{4 x-x^2+x \log (x)+(4-x+\log (x)) \log (-4+x-\log (x))} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {e^4 \left (-1+17 x-4 x^2-12 x^3+3 x^4\right )+e^4 \left (4 x-3 x^3\right ) \log (x)+\left (e^4 \left (20-5 x-12 x^2+3 x^3\right )+e^4 \left (5-3 x^2\right ) \log (x)\right ) \log (-4+x-\log (x))+\left (e^4 \left (-4 x+x^2\right )-e^4 x \log (x)+\left (e^4 (-4+x)-e^4 \log (x)\right ) \log (-4+x-\log (x))\right ) \log (x+\log (-4+x-\log (x)))}{(4-x+\log (x)) (x+\log (-4+x-\log (x)))} \, dx \\ & = \int \frac {e^4 \left (-1+17 x-4 x^2-12 x^3+3 x^4+\left (4 x-3 x^3\right ) \log (x)+\left (-5+3 x^2\right ) (-4+x-\log (x)) \log (-4+x-\log (x))+(-4+x-\log (x)) (x+\log (-4+x-\log (x))) \log (x+\log (-4+x-\log (x)))\right )}{(4-x+\log (x)) (x+\log (-4+x-\log (x)))} \, dx \\ & = e^4 \int \frac {-1+17 x-4 x^2-12 x^3+3 x^4+\left (4 x-3 x^3\right ) \log (x)+\left (-5+3 x^2\right ) (-4+x-\log (x)) \log (-4+x-\log (x))+(-4+x-\log (x)) (x+\log (-4+x-\log (x))) \log (x+\log (-4+x-\log (x)))}{(4-x+\log (x)) (x+\log (-4+x-\log (x)))} \, dx \\ & = e^4 \int \left (\frac {1}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))}-\frac {17 x}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))}+\frac {4 x^2}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))}+\frac {12 x^3}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))}-\frac {3 x^4}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))}+\frac {x \left (-4+3 x^2\right ) \log (x)}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))}-\frac {\left (-5+3 x^2\right ) \log (-4+x-\log (x))}{x+\log (-4+x-\log (x))}-\log (x+\log (-4+x-\log (x)))\right ) \, dx \\ & = e^4 \int \frac {1}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))} \, dx+e^4 \int \frac {x \left (-4+3 x^2\right ) \log (x)}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))} \, dx-e^4 \int \frac {\left (-5+3 x^2\right ) \log (-4+x-\log (x))}{x+\log (-4+x-\log (x))} \, dx-e^4 \int \log (x+\log (-4+x-\log (x))) \, dx-\left (3 e^4\right ) \int \frac {x^4}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))} \, dx+\left (4 e^4\right ) \int \frac {x^2}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))} \, dx+\left (12 e^4\right ) \int \frac {x^3}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))} \, dx-\left (17 e^4\right ) \int \frac {x}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))} \, dx \\ & = e^4 \int \frac {1}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))} \, dx-e^4 \int \left (-5+3 x^2+\frac {x \left (5-3 x^2\right )}{x+\log (-4+x-\log (x))}\right ) \, dx+e^4 \int \left (-\frac {4 x \log (x)}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))}+\frac {3 x^3 \log (x)}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))}\right ) \, dx-e^4 \int \log (x+\log (-4+x-\log (x))) \, dx-\left (3 e^4\right ) \int \frac {x^4}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))} \, dx+\left (4 e^4\right ) \int \frac {x^2}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))} \, dx+\left (12 e^4\right ) \int \frac {x^3}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))} \, dx-\left (17 e^4\right ) \int \frac {x}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))} \, dx \\ & = 5 e^4 x-e^4 x^3-e^4 \int \frac {x \left (5-3 x^2\right )}{x+\log (-4+x-\log (x))} \, dx+e^4 \int \frac {1}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))} \, dx-e^4 \int \log (x+\log (-4+x-\log (x))) \, dx-\left (3 e^4\right ) \int \frac {x^4}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))} \, dx+\left (3 e^4\right ) \int \frac {x^3 \log (x)}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))} \, dx+\left (4 e^4\right ) \int \frac {x^2}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))} \, dx-\left (4 e^4\right ) \int \frac {x \log (x)}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))} \, dx+\left (12 e^4\right ) \int \frac {x^3}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))} \, dx-\left (17 e^4\right ) \int \frac {x}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))} \, dx \\ & = 5 e^4 x-e^4 x^3+e^4 \int \frac {1}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))} \, dx-e^4 \int \left (\frac {5 x}{x+\log (-4+x-\log (x))}-\frac {3 x^3}{x+\log (-4+x-\log (x))}\right ) \, dx-e^4 \int \log (x+\log (-4+x-\log (x))) \, dx-\left (3 e^4\right ) \int \frac {x^4}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))} \, dx+\left (3 e^4\right ) \int \frac {x^3 \log (x)}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))} \, dx+\left (4 e^4\right ) \int \frac {x^2}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))} \, dx-\left (4 e^4\right ) \int \frac {x \log (x)}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))} \, dx+\left (12 e^4\right ) \int \frac {x^3}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))} \, dx-\left (17 e^4\right ) \int \frac {x}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))} \, dx \\ & = 5 e^4 x-e^4 x^3+e^4 \int \frac {1}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))} \, dx-e^4 \int \log (x+\log (-4+x-\log (x))) \, dx+\left (3 e^4\right ) \int \frac {x^3}{x+\log (-4+x-\log (x))} \, dx-\left (3 e^4\right ) \int \frac {x^4}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))} \, dx+\left (3 e^4\right ) \int \frac {x^3 \log (x)}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))} \, dx+\left (4 e^4\right ) \int \frac {x^2}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))} \, dx-\left (4 e^4\right ) \int \frac {x \log (x)}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))} \, dx-\left (5 e^4\right ) \int \frac {x}{x+\log (-4+x-\log (x))} \, dx+\left (12 e^4\right ) \int \frac {x^3}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))} \, dx-\left (17 e^4\right ) \int \frac {x}{(-4+x-\log (x)) (x+\log (-4+x-\log (x)))} \, dx \\ \end{align*}
Time = 0.11 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.96 \[ \int \frac {e^4 \left (-1+17 x-4 x^2-12 x^3+3 x^4\right )+e^4 \left (4 x-3 x^3\right ) \log (x)+\left (e^4 \left (20-5 x-12 x^2+3 x^3\right )+e^4 \left (5-3 x^2\right ) \log (x)\right ) \log (-4+x-\log (x))+\left (e^4 \left (-4 x+x^2\right )-e^4 x \log (x)+\left (e^4 (-4+x)-e^4 \log (x)\right ) \log (-4+x-\log (x))\right ) \log (x+\log (-4+x-\log (x)))}{4 x-x^2+x \log (x)+(4-x+\log (x)) \log (-4+x-\log (x))} \, dx=e^4 \left (5 x-x^3-x \log (x+\log (-4+x-\log (x)))\right ) \]
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Time = 6.33 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.00
method | result | size |
risch | \(-x \,{\mathrm e}^{4} \ln \left (\ln \left (-\ln \left (x \right )+x -4\right )+x \right )-{\mathrm e}^{4} x \left (x^{2}-5\right )\) | \(28\) |
parallelrisch | \(-x^{3} {\mathrm e}^{4}-x \,{\mathrm e}^{4} \ln \left (\ln \left (-\ln \left (x \right )+x -4\right )+x \right )+5 x \,{\mathrm e}^{4}\) | \(30\) |
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Time = 0.26 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.00 \[ \int \frac {e^4 \left (-1+17 x-4 x^2-12 x^3+3 x^4\right )+e^4 \left (4 x-3 x^3\right ) \log (x)+\left (e^4 \left (20-5 x-12 x^2+3 x^3\right )+e^4 \left (5-3 x^2\right ) \log (x)\right ) \log (-4+x-\log (x))+\left (e^4 \left (-4 x+x^2\right )-e^4 x \log (x)+\left (e^4 (-4+x)-e^4 \log (x)\right ) \log (-4+x-\log (x))\right ) \log (x+\log (-4+x-\log (x)))}{4 x-x^2+x \log (x)+(4-x+\log (x)) \log (-4+x-\log (x))} \, dx=-x e^{4} \log \left (x + \log \left (x - \log \left (x\right ) - 4\right )\right ) - {\left (x^{3} - 5 \, x\right )} e^{4} \]
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Exception generated. \[ \int \frac {e^4 \left (-1+17 x-4 x^2-12 x^3+3 x^4\right )+e^4 \left (4 x-3 x^3\right ) \log (x)+\left (e^4 \left (20-5 x-12 x^2+3 x^3\right )+e^4 \left (5-3 x^2\right ) \log (x)\right ) \log (-4+x-\log (x))+\left (e^4 \left (-4 x+x^2\right )-e^4 x \log (x)+\left (e^4 (-4+x)-e^4 \log (x)\right ) \log (-4+x-\log (x))\right ) \log (x+\log (-4+x-\log (x)))}{4 x-x^2+x \log (x)+(4-x+\log (x)) \log (-4+x-\log (x))} \, dx=\text {Exception raised: TypeError} \]
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Time = 0.24 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.04 \[ \int \frac {e^4 \left (-1+17 x-4 x^2-12 x^3+3 x^4\right )+e^4 \left (4 x-3 x^3\right ) \log (x)+\left (e^4 \left (20-5 x-12 x^2+3 x^3\right )+e^4 \left (5-3 x^2\right ) \log (x)\right ) \log (-4+x-\log (x))+\left (e^4 \left (-4 x+x^2\right )-e^4 x \log (x)+\left (e^4 (-4+x)-e^4 \log (x)\right ) \log (-4+x-\log (x))\right ) \log (x+\log (-4+x-\log (x)))}{4 x-x^2+x \log (x)+(4-x+\log (x)) \log (-4+x-\log (x))} \, dx=-x^{3} e^{4} - x e^{4} \log \left (x + \log \left (x - \log \left (x\right ) - 4\right )\right ) + 5 \, x e^{4} \]
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Time = 0.34 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.04 \[ \int \frac {e^4 \left (-1+17 x-4 x^2-12 x^3+3 x^4\right )+e^4 \left (4 x-3 x^3\right ) \log (x)+\left (e^4 \left (20-5 x-12 x^2+3 x^3\right )+e^4 \left (5-3 x^2\right ) \log (x)\right ) \log (-4+x-\log (x))+\left (e^4 \left (-4 x+x^2\right )-e^4 x \log (x)+\left (e^4 (-4+x)-e^4 \log (x)\right ) \log (-4+x-\log (x))\right ) \log (x+\log (-4+x-\log (x)))}{4 x-x^2+x \log (x)+(4-x+\log (x)) \log (-4+x-\log (x))} \, dx=-x^{3} e^{4} - x e^{4} \log \left (x + \log \left (x - \log \left (x\right ) - 4\right )\right ) + 5 \, x e^{4} \]
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Time = 9.61 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.75 \[ \int \frac {e^4 \left (-1+17 x-4 x^2-12 x^3+3 x^4\right )+e^4 \left (4 x-3 x^3\right ) \log (x)+\left (e^4 \left (20-5 x-12 x^2+3 x^3\right )+e^4 \left (5-3 x^2\right ) \log (x)\right ) \log (-4+x-\log (x))+\left (e^4 \left (-4 x+x^2\right )-e^4 x \log (x)+\left (e^4 (-4+x)-e^4 \log (x)\right ) \log (-4+x-\log (x))\right ) \log (x+\log (-4+x-\log (x)))}{4 x-x^2+x \log (x)+(4-x+\log (x)) \log (-4+x-\log (x))} \, dx=-x\,{\mathrm {e}}^4\,\left (\ln \left (x+\ln \left (x-\ln \left (x\right )-4\right )\right )+x^2-5\right ) \]
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