Integrand size = 103, antiderivative size = 28 \[ \int \frac {-140 x+130 x^3+20 x^4+10 x^6+\left (40 x-40 x^3\right ) \log (x)+e^{e^x} \left (-70 x+10 x^4+e^x \left (-30 x^2-10 x^5\right )+\left (20 x+10 e^x x^2\right ) \log (x)\right )}{9+6 x^3+x^6+\left (-6-2 x^3\right ) \log (x)+\log ^2(x)} \, dx=\frac {10 x^2 \left (2+e^{e^x}-x^2\right )}{-3-x^3+\log (x)} \]
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\[ \int \frac {-140 x+130 x^3+20 x^4+10 x^6+\left (40 x-40 x^3\right ) \log (x)+e^{e^x} \left (-70 x+10 x^4+e^x \left (-30 x^2-10 x^5\right )+\left (20 x+10 e^x x^2\right ) \log (x)\right )}{9+6 x^3+x^6+\left (-6-2 x^3\right ) \log (x)+\log ^2(x)} \, dx=\int \frac {-140 x+130 x^3+20 x^4+10 x^6+\left (40 x-40 x^3\right ) \log (x)+e^{e^x} \left (-70 x+10 x^4+e^x \left (-30 x^2-10 x^5\right )+\left (20 x+10 e^x x^2\right ) \log (x)\right )}{9+6 x^3+x^6+\left (-6-2 x^3\right ) \log (x)+\log ^2(x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {-140 x+130 x^3+20 x^4+10 x^6+\left (40 x-40 x^3\right ) \log (x)+e^{e^x} \left (-70 x+10 x^4+e^x \left (-30 x^2-10 x^5\right )+\left (20 x+10 e^x x^2\right ) \log (x)\right )}{\left (3+x^3-\log (x)\right )^2} \, dx \\ & = \int \left (-\frac {140 x}{\left (3+x^3-\log (x)\right )^2}-\frac {70 e^{e^x} x}{\left (3+x^3-\log (x)\right )^2}+\frac {130 x^3}{\left (3+x^3-\log (x)\right )^2}+\frac {20 x^4}{\left (3+x^3-\log (x)\right )^2}+\frac {10 e^{e^x} x^4}{\left (3+x^3-\log (x)\right )^2}+\frac {10 x^6}{\left (3+x^3-\log (x)\right )^2}-\frac {10 e^{e^x+x} x^2}{3+x^3-\log (x)}+\frac {20 e^{e^x} x \log (x)}{\left (3+x^3-\log (x)\right )^2}-\frac {40 (-1+x) x (1+x) \log (x)}{\left (3+x^3-\log (x)\right )^2}\right ) \, dx \\ & = 10 \int \frac {e^{e^x} x^4}{\left (3+x^3-\log (x)\right )^2} \, dx+10 \int \frac {x^6}{\left (3+x^3-\log (x)\right )^2} \, dx-10 \int \frac {e^{e^x+x} x^2}{3+x^3-\log (x)} \, dx+20 \int \frac {x^4}{\left (3+x^3-\log (x)\right )^2} \, dx+20 \int \frac {e^{e^x} x \log (x)}{\left (3+x^3-\log (x)\right )^2} \, dx-40 \int \frac {(-1+x) x (1+x) \log (x)}{\left (3+x^3-\log (x)\right )^2} \, dx-70 \int \frac {e^{e^x} x}{\left (3+x^3-\log (x)\right )^2} \, dx+130 \int \frac {x^3}{\left (3+x^3-\log (x)\right )^2} \, dx-140 \int \frac {x}{\left (3+x^3-\log (x)\right )^2} \, dx \\ & = 10 \int \frac {e^{e^x} x^4}{\left (3+x^3-\log (x)\right )^2} \, dx+10 \int \frac {x^6}{\left (3+x^3-\log (x)\right )^2} \, dx-10 \int \frac {e^{e^x+x} x^2}{3+x^3-\log (x)} \, dx+20 \int \left (\frac {e^{e^x} x \left (3+x^3\right )}{\left (3+x^3-\log (x)\right )^2}-\frac {e^{e^x} x}{3+x^3-\log (x)}\right ) \, dx+20 \int \frac {x^4}{\left (3+x^3-\log (x)\right )^2} \, dx-40 \int \left (\frac {x \left (-3+3 x^2-x^3+x^5\right )}{\left (3+x^3-\log (x)\right )^2}+\frac {x \left (1-x^2\right )}{3+x^3-\log (x)}\right ) \, dx-70 \int \frac {e^{e^x} x}{\left (3+x^3-\log (x)\right )^2} \, dx+130 \int \frac {x^3}{\left (3+x^3-\log (x)\right )^2} \, dx-140 \int \frac {x}{\left (3+x^3-\log (x)\right )^2} \, dx \\ & = 10 \int \frac {e^{e^x} x^4}{\left (3+x^3-\log (x)\right )^2} \, dx+10 \int \frac {x^6}{\left (3+x^3-\log (x)\right )^2} \, dx-10 \int \frac {e^{e^x+x} x^2}{3+x^3-\log (x)} \, dx+20 \int \frac {x^4}{\left (3+x^3-\log (x)\right )^2} \, dx+20 \int \frac {e^{e^x} x \left (3+x^3\right )}{\left (3+x^3-\log (x)\right )^2} \, dx-20 \int \frac {e^{e^x} x}{3+x^3-\log (x)} \, dx-40 \int \frac {x \left (-3+3 x^2-x^3+x^5\right )}{\left (3+x^3-\log (x)\right )^2} \, dx-40 \int \frac {x \left (1-x^2\right )}{3+x^3-\log (x)} \, dx-70 \int \frac {e^{e^x} x}{\left (3+x^3-\log (x)\right )^2} \, dx+130 \int \frac {x^3}{\left (3+x^3-\log (x)\right )^2} \, dx-140 \int \frac {x}{\left (3+x^3-\log (x)\right )^2} \, dx \\ & = 10 \int \frac {e^{e^x} x^4}{\left (3+x^3-\log (x)\right )^2} \, dx+10 \int \frac {x^6}{\left (3+x^3-\log (x)\right )^2} \, dx-10 \int \frac {e^{e^x+x} x^2}{3+x^3-\log (x)} \, dx+20 \int \left (\frac {3 e^{e^x} x}{\left (3+x^3-\log (x)\right )^2}+\frac {e^{e^x} x^4}{\left (3+x^3-\log (x)\right )^2}\right ) \, dx+20 \int \frac {x^4}{\left (3+x^3-\log (x)\right )^2} \, dx-20 \int \frac {e^{e^x} x}{3+x^3-\log (x)} \, dx-40 \int \left (-\frac {3 x}{\left (3+x^3-\log (x)\right )^2}+\frac {3 x^3}{\left (3+x^3-\log (x)\right )^2}-\frac {x^4}{\left (3+x^3-\log (x)\right )^2}+\frac {x^6}{\left (3+x^3-\log (x)\right )^2}\right ) \, dx-40 \int \left (\frac {x}{3+x^3-\log (x)}-\frac {x^3}{3+x^3-\log (x)}\right ) \, dx-70 \int \frac {e^{e^x} x}{\left (3+x^3-\log (x)\right )^2} \, dx+130 \int \frac {x^3}{\left (3+x^3-\log (x)\right )^2} \, dx-140 \int \frac {x}{\left (3+x^3-\log (x)\right )^2} \, dx \\ & = 10 \int \frac {e^{e^x} x^4}{\left (3+x^3-\log (x)\right )^2} \, dx+10 \int \frac {x^6}{\left (3+x^3-\log (x)\right )^2} \, dx-10 \int \frac {e^{e^x+x} x^2}{3+x^3-\log (x)} \, dx+20 \int \frac {x^4}{\left (3+x^3-\log (x)\right )^2} \, dx+20 \int \frac {e^{e^x} x^4}{\left (3+x^3-\log (x)\right )^2} \, dx-20 \int \frac {e^{e^x} x}{3+x^3-\log (x)} \, dx+40 \int \frac {x^4}{\left (3+x^3-\log (x)\right )^2} \, dx-40 \int \frac {x^6}{\left (3+x^3-\log (x)\right )^2} \, dx-40 \int \frac {x}{3+x^3-\log (x)} \, dx+40 \int \frac {x^3}{3+x^3-\log (x)} \, dx+60 \int \frac {e^{e^x} x}{\left (3+x^3-\log (x)\right )^2} \, dx-70 \int \frac {e^{e^x} x}{\left (3+x^3-\log (x)\right )^2} \, dx+120 \int \frac {x}{\left (3+x^3-\log (x)\right )^2} \, dx-120 \int \frac {x^3}{\left (3+x^3-\log (x)\right )^2} \, dx+130 \int \frac {x^3}{\left (3+x^3-\log (x)\right )^2} \, dx-140 \int \frac {x}{\left (3+x^3-\log (x)\right )^2} \, dx \\ \end{align*}
Time = 0.08 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.00 \[ \int \frac {-140 x+130 x^3+20 x^4+10 x^6+\left (40 x-40 x^3\right ) \log (x)+e^{e^x} \left (-70 x+10 x^4+e^x \left (-30 x^2-10 x^5\right )+\left (20 x+10 e^x x^2\right ) \log (x)\right )}{9+6 x^3+x^6+\left (-6-2 x^3\right ) \log (x)+\log ^2(x)} \, dx=\frac {10 x^2 \left (-2-e^{e^x}+x^2\right )}{3+x^3-\log (x)} \]
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Time = 6.38 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.14
method | result | size |
parallelrisch | \(\frac {10 x^{4}-10 \,{\mathrm e}^{{\mathrm e}^{x}} x^{2}-20 x^{2}}{x^{3}-\ln \left (x \right )+3}\) | \(32\) |
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Time = 0.27 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.07 \[ \int \frac {-140 x+130 x^3+20 x^4+10 x^6+\left (40 x-40 x^3\right ) \log (x)+e^{e^x} \left (-70 x+10 x^4+e^x \left (-30 x^2-10 x^5\right )+\left (20 x+10 e^x x^2\right ) \log (x)\right )}{9+6 x^3+x^6+\left (-6-2 x^3\right ) \log (x)+\log ^2(x)} \, dx=\frac {10 \, {\left (x^{4} - x^{2} e^{\left (e^{x}\right )} - 2 \, x^{2}\right )}}{x^{3} - \log \left (x\right ) + 3} \]
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Time = 0.15 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.29 \[ \int \frac {-140 x+130 x^3+20 x^4+10 x^6+\left (40 x-40 x^3\right ) \log (x)+e^{e^x} \left (-70 x+10 x^4+e^x \left (-30 x^2-10 x^5\right )+\left (20 x+10 e^x x^2\right ) \log (x)\right )}{9+6 x^3+x^6+\left (-6-2 x^3\right ) \log (x)+\log ^2(x)} \, dx=- \frac {10 x^{2} e^{e^{x}}}{x^{3} - \log {\left (x \right )} + 3} + \frac {- 10 x^{4} + 20 x^{2}}{- x^{3} + \log {\left (x \right )} - 3} \]
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Time = 0.22 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.07 \[ \int \frac {-140 x+130 x^3+20 x^4+10 x^6+\left (40 x-40 x^3\right ) \log (x)+e^{e^x} \left (-70 x+10 x^4+e^x \left (-30 x^2-10 x^5\right )+\left (20 x+10 e^x x^2\right ) \log (x)\right )}{9+6 x^3+x^6+\left (-6-2 x^3\right ) \log (x)+\log ^2(x)} \, dx=\frac {10 \, {\left (x^{4} - x^{2} e^{\left (e^{x}\right )} - 2 \, x^{2}\right )}}{x^{3} - \log \left (x\right ) + 3} \]
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Time = 0.29 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.61 \[ \int \frac {-140 x+130 x^3+20 x^4+10 x^6+\left (40 x-40 x^3\right ) \log (x)+e^{e^x} \left (-70 x+10 x^4+e^x \left (-30 x^2-10 x^5\right )+\left (20 x+10 e^x x^2\right ) \log (x)\right )}{9+6 x^3+x^6+\left (-6-2 x^3\right ) \log (x)+\log ^2(x)} \, dx=\frac {10 \, {\left (x^{4} e^{x} - x^{2} e^{\left (x + e^{x}\right )} - 2 \, x^{2} e^{x}\right )}}{x^{3} e^{x} - e^{x} \log \left (x\right ) + 3 \, e^{x}} \]
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Time = 14.34 (sec) , antiderivative size = 104, normalized size of antiderivative = 3.71 \[ \int \frac {-140 x+130 x^3+20 x^4+10 x^6+\left (40 x-40 x^3\right ) \log (x)+e^{e^x} \left (-70 x+10 x^4+e^x \left (-30 x^2-10 x^5\right )+\left (20 x+10 e^x x^2\right ) \log (x)\right )}{9+6 x^3+x^6+\left (-6-2 x^3\right ) \log (x)+\log ^2(x)} \, dx=\frac {40\,x}{3}+\frac {\frac {40\,x}{9}-\frac {40\,x^2}{3}}{x^3-\frac {1}{3}}-\frac {\frac {10\,x^2\,\left (x^5+2\,x^3+13\,x^2-14\right )}{3\,x^3-1}-\frac {40\,x^2\,\ln \left (x\right )\,\left (x^2-1\right )}{3\,x^3-1}}{x^3-\ln \left (x\right )+3}-\frac {10\,x^2\,{\mathrm {e}}^{{\mathrm {e}}^x}}{x^3-\ln \left (x\right )+3} \]
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