Integrand size = 172, antiderivative size = 24 \[ \int \frac {2-2 x+15 x^2+15 x^3+50 x^5+\left (-20 x^2-50 x^4\right ) \log \left (2 x+5 x^3\right )+\left (-4 x^3-10 x^5+\left (4 x^2+10 x^4\right ) \log \left (2 x+5 x^3\right )\right ) \log \left (x-\log \left (2 x+5 x^3\right )\right )}{10 x^2+25 x^4+\left (-10 x-25 x^3\right ) \log \left (2 x+5 x^3\right )+\left (-2 x^2-5 x^4+\left (2 x+5 x^3\right ) \log \left (2 x+5 x^3\right )\right ) \log \left (x-\log \left (2 x+5 x^3\right )\right )} \, dx=x^2+\log \left (-5+\log \left (x-\log \left (x+x \left (1+5 x^2\right )\right )\right )\right ) \]
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\[ \int \frac {2-2 x+15 x^2+15 x^3+50 x^5+\left (-20 x^2-50 x^4\right ) \log \left (2 x+5 x^3\right )+\left (-4 x^3-10 x^5+\left (4 x^2+10 x^4\right ) \log \left (2 x+5 x^3\right )\right ) \log \left (x-\log \left (2 x+5 x^3\right )\right )}{10 x^2+25 x^4+\left (-10 x-25 x^3\right ) \log \left (2 x+5 x^3\right )+\left (-2 x^2-5 x^4+\left (2 x+5 x^3\right ) \log \left (2 x+5 x^3\right )\right ) \log \left (x-\log \left (2 x+5 x^3\right )\right )} \, dx=\int \frac {2-2 x+15 x^2+15 x^3+50 x^5+\left (-20 x^2-50 x^4\right ) \log \left (2 x+5 x^3\right )+\left (-4 x^3-10 x^5+\left (4 x^2+10 x^4\right ) \log \left (2 x+5 x^3\right )\right ) \log \left (x-\log \left (2 x+5 x^3\right )\right )}{10 x^2+25 x^4+\left (-10 x-25 x^3\right ) \log \left (2 x+5 x^3\right )+\left (-2 x^2-5 x^4+\left (2 x+5 x^3\right ) \log \left (2 x+5 x^3\right )\right ) \log \left (x-\log \left (2 x+5 x^3\right )\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {2-2 x+15 x^2+15 x^3+50 x^5+\left (-20 x^2-50 x^4\right ) \log \left (2 x+5 x^3\right )+\left (-4 x^3-10 x^5+\left (4 x^2+10 x^4\right ) \log \left (2 x+5 x^3\right )\right ) \log \left (x-\log \left (2 x+5 x^3\right )\right )}{x \left (2+5 x^2\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (5-\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )} \, dx \\ & = \int \left (\frac {2}{\left (2+5 x^2\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )}-\frac {2}{x \left (2+5 x^2\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )}-\frac {15 x}{\left (2+5 x^2\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )}-\frac {15 x^2}{\left (2+5 x^2\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )}-\frac {50 x^4}{\left (2+5 x^2\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )}+\frac {10 x \log \left (x \left (2+5 x^2\right )\right )}{\left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )}+\frac {2 x \log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )}{-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )}\right ) \, dx \\ & = 2 \int \frac {1}{\left (2+5 x^2\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )} \, dx-2 \int \frac {1}{x \left (2+5 x^2\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )} \, dx+2 \int \frac {x \log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )}{-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )} \, dx+10 \int \frac {x \log \left (x \left (2+5 x^2\right )\right )}{\left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )} \, dx-15 \int \frac {x}{\left (2+5 x^2\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )} \, dx-15 \int \frac {x^2}{\left (2+5 x^2\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )} \, dx-50 \int \frac {x^4}{\left (2+5 x^2\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )} \, dx \\ & = 2 \int \left (x+\frac {5 x}{-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )}\right ) \, dx+2 \int \left (\frac {i}{2 \sqrt {2} \left (i \sqrt {2}-\sqrt {5} x\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )}+\frac {i}{2 \sqrt {2} \left (i \sqrt {2}+\sqrt {5} x\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )}\right ) \, dx-2 \int \left (\frac {1}{2 x \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )}-\frac {5 x}{2 \left (2+5 x^2\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )}\right ) \, dx+10 \int \frac {x \log \left (x \left (2+5 x^2\right )\right )}{\left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )} \, dx-15 \int \left (-\frac {1}{2 \sqrt {5} \left (i \sqrt {2}-\sqrt {5} x\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )}+\frac {1}{2 \sqrt {5} \left (i \sqrt {2}+\sqrt {5} x\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )}\right ) \, dx-15 \int \left (\frac {1}{5 \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )}-\frac {2}{5 \left (2+5 x^2\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )}\right ) \, dx-50 \int \left (-\frac {2}{25 \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )}+\frac {x^2}{5 \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )}+\frac {4}{25 \left (2+5 x^2\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )}\right ) \, dx \\ & = x^2-3 \int \frac {1}{\left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )} \, dx+4 \int \frac {1}{\left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )} \, dx+5 \int \frac {x}{\left (2+5 x^2\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )} \, dx+6 \int \frac {1}{\left (2+5 x^2\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )} \, dx-8 \int \frac {1}{\left (2+5 x^2\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )} \, dx+10 \int \frac {x}{-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )} \, dx-10 \int \frac {x^2}{\left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )} \, dx+10 \int \frac {x \log \left (x \left (2+5 x^2\right )\right )}{\left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )} \, dx+\frac {i \int \frac {1}{\left (i \sqrt {2}-\sqrt {5} x\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )} \, dx}{\sqrt {2}}+\frac {i \int \frac {1}{\left (i \sqrt {2}+\sqrt {5} x\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )} \, dx}{\sqrt {2}}+\frac {1}{2} \left (3 \sqrt {5}\right ) \int \frac {1}{\left (i \sqrt {2}-\sqrt {5} x\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )} \, dx-\frac {1}{2} \left (3 \sqrt {5}\right ) \int \frac {1}{\left (i \sqrt {2}+\sqrt {5} x\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )} \, dx-\int \frac {1}{x \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )} \, dx \\ & = x^2-3 \int \frac {1}{\left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )} \, dx+4 \int \frac {1}{\left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )} \, dx+5 \int \left (-\frac {1}{2 \sqrt {5} \left (i \sqrt {2}-\sqrt {5} x\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )}+\frac {1}{2 \sqrt {5} \left (i \sqrt {2}+\sqrt {5} x\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )}\right ) \, dx+6 \int \left (\frac {i}{2 \sqrt {2} \left (i \sqrt {2}-\sqrt {5} x\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )}+\frac {i}{2 \sqrt {2} \left (i \sqrt {2}+\sqrt {5} x\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )}\right ) \, dx-8 \int \left (\frac {i}{2 \sqrt {2} \left (i \sqrt {2}-\sqrt {5} x\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )}+\frac {i}{2 \sqrt {2} \left (i \sqrt {2}+\sqrt {5} x\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )}\right ) \, dx+10 \int \frac {x}{-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )} \, dx-10 \int \frac {x^2}{\left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )} \, dx+10 \int \frac {x \log \left (x \left (2+5 x^2\right )\right )}{\left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )} \, dx+\frac {i \int \frac {1}{\left (i \sqrt {2}-\sqrt {5} x\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )} \, dx}{\sqrt {2}}+\frac {i \int \frac {1}{\left (i \sqrt {2}+\sqrt {5} x\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )} \, dx}{\sqrt {2}}+\frac {1}{2} \left (3 \sqrt {5}\right ) \int \frac {1}{\left (i \sqrt {2}-\sqrt {5} x\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )} \, dx-\frac {1}{2} \left (3 \sqrt {5}\right ) \int \frac {1}{\left (i \sqrt {2}+\sqrt {5} x\right ) \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )} \, dx-\int \frac {1}{x \left (x-\log \left (x \left (2+5 x^2\right )\right )\right ) \left (-5+\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right )} \, dx \\ & = \text {Too large to display} \\ \end{align*}
Time = 0.10 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00 \[ \int \frac {2-2 x+15 x^2+15 x^3+50 x^5+\left (-20 x^2-50 x^4\right ) \log \left (2 x+5 x^3\right )+\left (-4 x^3-10 x^5+\left (4 x^2+10 x^4\right ) \log \left (2 x+5 x^3\right )\right ) \log \left (x-\log \left (2 x+5 x^3\right )\right )}{10 x^2+25 x^4+\left (-10 x-25 x^3\right ) \log \left (2 x+5 x^3\right )+\left (-2 x^2-5 x^4+\left (2 x+5 x^3\right ) \log \left (2 x+5 x^3\right )\right ) \log \left (x-\log \left (2 x+5 x^3\right )\right )} \, dx=x^2+\log \left (5-\log \left (x-\log \left (x \left (2+5 x^2\right )\right )\right )\right ) \]
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Time = 2.51 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00
method | result | size |
parallelrisch | \(-\frac {1}{5}+x^{2}+\ln \left (\ln \left (-\ln \left (5 x^{3}+2 x \right )+x \right )-5\right )\) | \(24\) |
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Time = 0.26 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.92 \[ \int \frac {2-2 x+15 x^2+15 x^3+50 x^5+\left (-20 x^2-50 x^4\right ) \log \left (2 x+5 x^3\right )+\left (-4 x^3-10 x^5+\left (4 x^2+10 x^4\right ) \log \left (2 x+5 x^3\right )\right ) \log \left (x-\log \left (2 x+5 x^3\right )\right )}{10 x^2+25 x^4+\left (-10 x-25 x^3\right ) \log \left (2 x+5 x^3\right )+\left (-2 x^2-5 x^4+\left (2 x+5 x^3\right ) \log \left (2 x+5 x^3\right )\right ) \log \left (x-\log \left (2 x+5 x^3\right )\right )} \, dx=x^{2} + \log \left (\log \left (x - \log \left (5 \, x^{3} + 2 \, x\right )\right ) - 5\right ) \]
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Time = 0.32 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.79 \[ \int \frac {2-2 x+15 x^2+15 x^3+50 x^5+\left (-20 x^2-50 x^4\right ) \log \left (2 x+5 x^3\right )+\left (-4 x^3-10 x^5+\left (4 x^2+10 x^4\right ) \log \left (2 x+5 x^3\right )\right ) \log \left (x-\log \left (2 x+5 x^3\right )\right )}{10 x^2+25 x^4+\left (-10 x-25 x^3\right ) \log \left (2 x+5 x^3\right )+\left (-2 x^2-5 x^4+\left (2 x+5 x^3\right ) \log \left (2 x+5 x^3\right )\right ) \log \left (x-\log \left (2 x+5 x^3\right )\right )} \, dx=x^{2} + \log {\left (\log {\left (x - \log {\left (5 x^{3} + 2 x \right )} \right )} - 5 \right )} \]
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Time = 0.25 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00 \[ \int \frac {2-2 x+15 x^2+15 x^3+50 x^5+\left (-20 x^2-50 x^4\right ) \log \left (2 x+5 x^3\right )+\left (-4 x^3-10 x^5+\left (4 x^2+10 x^4\right ) \log \left (2 x+5 x^3\right )\right ) \log \left (x-\log \left (2 x+5 x^3\right )\right )}{10 x^2+25 x^4+\left (-10 x-25 x^3\right ) \log \left (2 x+5 x^3\right )+\left (-2 x^2-5 x^4+\left (2 x+5 x^3\right ) \log \left (2 x+5 x^3\right )\right ) \log \left (x-\log \left (2 x+5 x^3\right )\right )} \, dx=x^{2} + \log \left (\log \left (x - \log \left (5 \, x^{2} + 2\right ) - \log \left (x\right )\right ) - 5\right ) \]
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Time = 0.46 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.92 \[ \int \frac {2-2 x+15 x^2+15 x^3+50 x^5+\left (-20 x^2-50 x^4\right ) \log \left (2 x+5 x^3\right )+\left (-4 x^3-10 x^5+\left (4 x^2+10 x^4\right ) \log \left (2 x+5 x^3\right )\right ) \log \left (x-\log \left (2 x+5 x^3\right )\right )}{10 x^2+25 x^4+\left (-10 x-25 x^3\right ) \log \left (2 x+5 x^3\right )+\left (-2 x^2-5 x^4+\left (2 x+5 x^3\right ) \log \left (2 x+5 x^3\right )\right ) \log \left (x-\log \left (2 x+5 x^3\right )\right )} \, dx=x^{2} + \log \left (\log \left (x - \log \left (5 \, x^{3} + 2 \, x\right )\right ) - 5\right ) \]
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Time = 13.31 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.92 \[ \int \frac {2-2 x+15 x^2+15 x^3+50 x^5+\left (-20 x^2-50 x^4\right ) \log \left (2 x+5 x^3\right )+\left (-4 x^3-10 x^5+\left (4 x^2+10 x^4\right ) \log \left (2 x+5 x^3\right )\right ) \log \left (x-\log \left (2 x+5 x^3\right )\right )}{10 x^2+25 x^4+\left (-10 x-25 x^3\right ) \log \left (2 x+5 x^3\right )+\left (-2 x^2-5 x^4+\left (2 x+5 x^3\right ) \log \left (2 x+5 x^3\right )\right ) \log \left (x-\log \left (2 x+5 x^3\right )\right )} \, dx=\ln \left (\ln \left (x-\ln \left (5\,x^3+2\,x\right )\right )-5\right )+x^2 \]
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