Integrand size = 160, antiderivative size = 27 \[ \int \frac {3 x^3-x^4+\left (3 x+x^2\right ) \log \left (\frac {16}{5}\right )+\left (2 x^4-2 x^2 \log \left (\frac {16}{5}\right )+\left (-6 x^3+6 x \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log \left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}{\left (x^3-x \log \left (\frac {16}{5}\right )+\left (-3 x^2+3 \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx=\frac {x^2}{\log \left (\frac {x}{3}-\log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )} \]
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\[ \int \frac {3 x^3-x^4+\left (3 x+x^2\right ) \log \left (\frac {16}{5}\right )+\left (2 x^4-2 x^2 \log \left (\frac {16}{5}\right )+\left (-6 x^3+6 x \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log \left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}{\left (x^3-x \log \left (\frac {16}{5}\right )+\left (-3 x^2+3 \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx=\int \frac {3 x^3-x^4+\left (3 x+x^2\right ) \log \left (\frac {16}{5}\right )+\left (2 x^4-2 x^2 \log \left (\frac {16}{5}\right )+\left (-6 x^3+6 x \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log \left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}{\left (x^3-x \log \left (\frac {16}{5}\right )+\left (-3 x^2+3 \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {3 x^3-x^4+\left (3 x+x^2\right ) \log \left (\frac {16}{5}\right )+\left (2 x^4-2 x^2 \log \left (\frac {16}{5}\right )+\left (-6 x^3+6 x \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log \left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}{\left (x^2-\log \left (\frac {16}{5}\right )\right ) \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx \\ & = \int \left (-\frac {x \left (-3 x^2+x^3-3 \log \left (\frac {16}{5}\right )-x \log \left (\frac {16}{5}\right )\right )}{\left (x^2-\log \left (\frac {16}{5}\right )\right ) \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}+\frac {2 x}{\log \left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}\right ) \, dx \\ & = 2 \int \frac {x}{\log \left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx-\int \frac {x \left (-3 x^2+x^3-3 \log \left (\frac {16}{5}\right )-x \log \left (\frac {16}{5}\right )\right )}{\left (x^2-\log \left (\frac {16}{5}\right )\right ) \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx \\ & = 2 \int \frac {x}{\log \left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx-\int \left (-\frac {3 x}{\left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}+\frac {x^2}{\left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}-\frac {6 x \log \left (\frac {16}{5}\right )}{\left (x^2-\log \left (\frac {16}{5}\right )\right ) \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}\right ) \, dx \\ & = 2 \int \frac {x}{\log \left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx+3 \int \frac {x}{\left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx+\left (6 \log \left (\frac {16}{5}\right )\right ) \int \frac {x}{\left (x^2-\log \left (\frac {16}{5}\right )\right ) \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx-\int \frac {x^2}{\left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx \\ & = 2 \int \frac {x}{\log \left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx+3 \int \frac {x}{\left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx+\left (6 \log \left (\frac {16}{5}\right )\right ) \int \left (-\frac {1}{2 \left (-x+\sqrt {\log \left (\frac {16}{5}\right )}\right ) \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}+\frac {1}{2 \left (x+\sqrt {\log \left (\frac {16}{5}\right )}\right ) \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}\right ) \, dx-\int \frac {x^2}{\left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx \\ & = 2 \int \frac {x}{\log \left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx+3 \int \frac {x}{\left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx-\left (3 \log \left (\frac {16}{5}\right )\right ) \int \frac {1}{\left (-x+\sqrt {\log \left (\frac {16}{5}\right )}\right ) \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx+\left (3 \log \left (\frac {16}{5}\right )\right ) \int \frac {1}{\left (x+\sqrt {\log \left (\frac {16}{5}\right )}\right ) \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx-\int \frac {x^2}{\left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx \\ \end{align*}
Time = 0.06 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.00 \[ \int \frac {3 x^3-x^4+\left (3 x+x^2\right ) \log \left (\frac {16}{5}\right )+\left (2 x^4-2 x^2 \log \left (\frac {16}{5}\right )+\left (-6 x^3+6 x \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log \left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}{\left (x^3-x \log \left (\frac {16}{5}\right )+\left (-3 x^2+3 \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx=\frac {x^2}{\log \left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \]
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Time = 2.88 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.04
method | result | size |
parallelrisch | \(\frac {x^{2}}{\ln \left (-\ln \left (-\frac {-x^{2}+\ln \left (\frac {16}{5}\right )}{x}\right )+\frac {x}{3}\right )}\) | \(28\) |
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Time = 0.26 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.96 \[ \int \frac {3 x^3-x^4+\left (3 x+x^2\right ) \log \left (\frac {16}{5}\right )+\left (2 x^4-2 x^2 \log \left (\frac {16}{5}\right )+\left (-6 x^3+6 x \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log \left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}{\left (x^3-x \log \left (\frac {16}{5}\right )+\left (-3 x^2+3 \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx=\frac {x^{2}}{\log \left (\frac {1}{3} \, x - \log \left (\frac {x^{2} - \log \left (\frac {16}{5}\right )}{x}\right )\right )} \]
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Time = 0.30 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.70 \[ \int \frac {3 x^3-x^4+\left (3 x+x^2\right ) \log \left (\frac {16}{5}\right )+\left (2 x^4-2 x^2 \log \left (\frac {16}{5}\right )+\left (-6 x^3+6 x \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log \left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}{\left (x^3-x \log \left (\frac {16}{5}\right )+\left (-3 x^2+3 \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx=\frac {x^{2}}{\log {\left (\frac {x}{3} - \log {\left (\frac {x^{2} - \log {\left (\frac {16}{5} \right )}}{x} \right )} \right )}} \]
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Time = 0.31 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.19 \[ \int \frac {3 x^3-x^4+\left (3 x+x^2\right ) \log \left (\frac {16}{5}\right )+\left (2 x^4-2 x^2 \log \left (\frac {16}{5}\right )+\left (-6 x^3+6 x \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log \left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}{\left (x^3-x \log \left (\frac {16}{5}\right )+\left (-3 x^2+3 \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx=-\frac {x^{2}}{\log \left (3\right ) - \log \left (x - 3 \, \log \left (x^{2} + \log \left (5\right ) - 4 \, \log \left (2\right )\right ) + 3 \, \log \left (x\right )\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 1559 vs. \(2 (23) = 46\).
Time = 1.07 (sec) , antiderivative size = 1559, normalized size of antiderivative = 57.74 \[ \int \frac {3 x^3-x^4+\left (3 x+x^2\right ) \log \left (\frac {16}{5}\right )+\left (2 x^4-2 x^2 \log \left (\frac {16}{5}\right )+\left (-6 x^3+6 x \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log \left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}{\left (x^3-x \log \left (\frac {16}{5}\right )+\left (-3 x^2+3 \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx=\text {Too large to display} \]
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Timed out. \[ \int \frac {3 x^3-x^4+\left (3 x+x^2\right ) \log \left (\frac {16}{5}\right )+\left (2 x^4-2 x^2 \log \left (\frac {16}{5}\right )+\left (-6 x^3+6 x \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log \left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}{\left (x^3-x \log \left (\frac {16}{5}\right )+\left (-3 x^2+3 \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx=\int \frac {\ln \left (\frac {x}{3}-\ln \left (-\frac {\ln \left (\frac {16}{5}\right )-x^2}{x}\right )\right )\,\left (2\,x^4-2\,x^2\,\ln \left (\frac {16}{5}\right )+\ln \left (-\frac {\ln \left (\frac {16}{5}\right )-x^2}{x}\right )\,\left (6\,x\,\ln \left (\frac {16}{5}\right )-6\,x^3\right )\right )+3\,x^3-x^4+\ln \left (\frac {16}{5}\right )\,\left (x^2+3\,x\right )}{{\ln \left (\frac {x}{3}-\ln \left (-\frac {\ln \left (\frac {16}{5}\right )-x^2}{x}\right )\right )}^2\,\left (\ln \left (-\frac {\ln \left (\frac {16}{5}\right )-x^2}{x}\right )\,\left (3\,\ln \left (\frac {16}{5}\right )-3\,x^2\right )-x\,\ln \left (\frac {16}{5}\right )+x^3\right )} \,d x \]
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