Integrand size = 46, antiderivative size = 20 \[ \int \frac {8+30 x^3}{\left (-10 x-40 x^3+75 x^4\right ) \log \left (\frac {-2-8 x^2+15 x^3}{2 x^2}\right )} \, dx=\frac {1}{5} \log \left (\log ^2\left (-4-\frac {1}{x^2}+\frac {15 x}{2}\right )\right ) \]
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Time = 0.08 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.25, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {1608, 6816} \[ \int \frac {8+30 x^3}{\left (-10 x-40 x^3+75 x^4\right ) \log \left (\frac {-2-8 x^2+15 x^3}{2 x^2}\right )} \, dx=\frac {2}{5} \log \left (\log \left (-\frac {-15 x^3+8 x^2+2}{2 x^2}\right )\right ) \]
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Rule 1608
Rule 6816
Rubi steps \begin{align*} \text {integral}& = \int \frac {8+30 x^3}{x \left (-10-40 x^2+75 x^3\right ) \log \left (\frac {-2-8 x^2+15 x^3}{2 x^2}\right )} \, dx \\ & = \frac {2}{5} \log \left (\log \left (-\frac {2+8 x^2-15 x^3}{2 x^2}\right )\right ) \\ \end{align*}
Time = 0.08 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.90 \[ \int \frac {8+30 x^3}{\left (-10 x-40 x^3+75 x^4\right ) \log \left (\frac {-2-8 x^2+15 x^3}{2 x^2}\right )} \, dx=\frac {2}{5} \log \left (\log \left (-4-\frac {1}{x^2}+\frac {15 x}{2}\right )\right ) \]
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Time = 0.09 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10
method | result | size |
norman | \(\frac {2 \ln \left (\ln \left (\frac {15 x^{3}-8 x^{2}-2}{2 x^{2}}\right )\right )}{5}\) | \(22\) |
risch | \(\frac {2 \ln \left (\ln \left (\frac {15 x^{3}-8 x^{2}-2}{2 x^{2}}\right )\right )}{5}\) | \(22\) |
parallelrisch | \(\frac {2 \ln \left (\ln \left (\frac {15 x^{3}-8 x^{2}-2}{2 x^{2}}\right )\right )}{5}\) | \(22\) |
default | \(\frac {2 \ln \left (\ln \left (2\right )-\ln \left (\frac {15 x^{3}-8 x^{2}-2}{x^{2}}\right )\right )}{5}\) | \(26\) |
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Time = 0.24 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.05 \[ \int \frac {8+30 x^3}{\left (-10 x-40 x^3+75 x^4\right ) \log \left (\frac {-2-8 x^2+15 x^3}{2 x^2}\right )} \, dx=\frac {2}{5} \, \log \left (\log \left (\frac {15 \, x^{3} - 8 \, x^{2} - 2}{2 \, x^{2}}\right )\right ) \]
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Time = 0.17 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10 \[ \int \frac {8+30 x^3}{\left (-10 x-40 x^3+75 x^4\right ) \log \left (\frac {-2-8 x^2+15 x^3}{2 x^2}\right )} \, dx=\frac {2 \log {\left (\log {\left (\frac {\frac {15 x^{3}}{2} - 4 x^{2} - 1}{x^{2}} \right )} \right )}}{5} \]
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Time = 0.31 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.25 \[ \int \frac {8+30 x^3}{\left (-10 x-40 x^3+75 x^4\right ) \log \left (\frac {-2-8 x^2+15 x^3}{2 x^2}\right )} \, dx=\frac {2}{5} \, \log \left (-\log \left (2\right ) + \log \left (15 \, x^{3} - 8 \, x^{2} - 2\right ) - 2 \, \log \left (x\right )\right ) \]
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Time = 0.27 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.05 \[ \int \frac {8+30 x^3}{\left (-10 x-40 x^3+75 x^4\right ) \log \left (\frac {-2-8 x^2+15 x^3}{2 x^2}\right )} \, dx=\frac {2}{5} \, \log \left (\log \left (\frac {15 \, x^{3} - 8 \, x^{2} - 2}{2 \, x^{2}}\right )\right ) \]
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Time = 9.57 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.05 \[ \int \frac {8+30 x^3}{\left (-10 x-40 x^3+75 x^4\right ) \log \left (\frac {-2-8 x^2+15 x^3}{2 x^2}\right )} \, dx=\frac {2\,\ln \left (\ln \left (-\frac {-15\,x^3+8\,x^2+2}{2\,x^2}\right )\right )}{5} \]
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