Integrand size = 99, antiderivative size = 24 \[ \int \frac {\left (37500-15036 x-2484 x^2+4 x^3+\left (30000-15048 x+24 x^2\right ) \log (625-x)\right ) \log \left (\frac {-30 x^2+10 x^3}{5+x+4 \log (625-x)}\right )}{9375 x-1265 x^2-623 x^3+x^4+\left (7500 x-2512 x^2+4 x^3\right ) \log (625-x)} \, dx=\log ^2\left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right ) \]
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\[ \int \frac {\left (37500-15036 x-2484 x^2+4 x^3+\left (30000-15048 x+24 x^2\right ) \log (625-x)\right ) \log \left (\frac {-30 x^2+10 x^3}{5+x+4 \log (625-x)}\right )}{9375 x-1265 x^2-623 x^3+x^4+\left (7500 x-2512 x^2+4 x^3\right ) \log (625-x)} \, dx=\int \frac {\left (37500-15036 x-2484 x^2+4 x^3+\left (30000-15048 x+24 x^2\right ) \log (625-x)\right ) \log \left (\frac {-30 x^2+10 x^3}{5+x+4 \log (625-x)}\right )}{9375 x-1265 x^2-623 x^3+x^4+\left (7500 x-2512 x^2+4 x^3\right ) \log (625-x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\left (37500-15036 x-2484 x^2+4 x^3+\left (30000-15048 x+24 x^2\right ) \log (625-x)\right ) \log \left (\frac {x^2 (-30+10 x)}{5+x+4 \log (625-x)}\right )}{x \left (1875-628 x+x^2\right ) (5+x+4 \log (625-x))} \, dx \\ & = \int \left (\frac {2 \left (9375-3759 x-621 x^2+x^3+7500 \log (625-x)-3762 x \log (625-x)+6 x^2 \log (625-x)\right ) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{194375 (-625+x) (5+x+4 \log (625-x))}-\frac {2 \left (9375-3759 x-621 x^2+x^3+7500 \log (625-x)-3762 x \log (625-x)+6 x^2 \log (625-x)\right ) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{933 (-3+x) (5+x+4 \log (625-x))}+\frac {4 \left (9375-3759 x-621 x^2+x^3+7500 \log (625-x)-3762 x \log (625-x)+6 x^2 \log (625-x)\right ) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{1875 x (5+x+4 \log (625-x))}\right ) \, dx \\ & = \frac {2 \int \frac {\left (9375-3759 x-621 x^2+x^3+7500 \log (625-x)-3762 x \log (625-x)+6 x^2 \log (625-x)\right ) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-625+x) (5+x+4 \log (625-x))} \, dx}{194375}+\frac {4 \int \frac {\left (9375-3759 x-621 x^2+x^3+7500 \log (625-x)-3762 x \log (625-x)+6 x^2 \log (625-x)\right ) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{x (5+x+4 \log (625-x))} \, dx}{1875}-\frac {2}{933} \int \frac {\left (9375-3759 x-621 x^2+x^3+7500 \log (625-x)-3762 x \log (625-x)+6 x^2 \log (625-x)\right ) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-3+x) (5+x+4 \log (625-x))} \, dx \\ & = \frac {2 \int \left (\frac {9375 \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-625+x) (5+x+4 \log (625-x))}-\frac {3759 x \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-625+x) (5+x+4 \log (625-x))}-\frac {621 x^2 \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-625+x) (5+x+4 \log (625-x))}+\frac {x^3 \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-625+x) (5+x+4 \log (625-x))}+\frac {7500 \log (625-x) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-625+x) (5+x+4 \log (625-x))}-\frac {3762 x \log (625-x) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-625+x) (5+x+4 \log (625-x))}+\frac {6 x^2 \log (625-x) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-625+x) (5+x+4 \log (625-x))}\right ) \, dx}{194375}+\frac {4 \int \frac {\left (9375-3759 x-621 x^2+x^3+6 \left (1250-627 x+x^2\right ) \log (625-x)\right ) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{x (5+x+4 \log (625-x))} \, dx}{1875}-\frac {2}{933} \int \left (\frac {9375 \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-3+x) (5+x+4 \log (625-x))}-\frac {3759 x \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-3+x) (5+x+4 \log (625-x))}-\frac {621 x^2 \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-3+x) (5+x+4 \log (625-x))}+\frac {x^3 \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-3+x) (5+x+4 \log (625-x))}+\frac {7500 \log (625-x) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-3+x) (5+x+4 \log (625-x))}-\frac {3762 x \log (625-x) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-3+x) (5+x+4 \log (625-x))}+\frac {6 x^2 \log (625-x) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-3+x) (5+x+4 \log (625-x))}\right ) \, dx \\ & = \frac {2 \int \frac {x^3 \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-625+x) (5+x+4 \log (625-x))} \, dx}{194375}+\frac {12 \int \frac {x^2 \log (625-x) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-625+x) (5+x+4 \log (625-x))} \, dx}{194375}+\frac {4 \int \left (-\frac {3759 \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{5+x+4 \log (625-x)}+\frac {9375 \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{x (5+x+4 \log (625-x))}-\frac {621 x \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{5+x+4 \log (625-x)}+\frac {x^2 \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{5+x+4 \log (625-x)}-\frac {3762 \log (625-x) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{5+x+4 \log (625-x)}+\frac {7500 \log (625-x) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{x (5+x+4 \log (625-x))}+\frac {6 x \log (625-x) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{5+x+4 \log (625-x)}\right ) \, dx}{1875}-\frac {2}{933} \int \frac {x^3 \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-3+x) (5+x+4 \log (625-x))} \, dx-\frac {1242 \int \frac {x^2 \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-625+x) (5+x+4 \log (625-x))} \, dx}{194375}-\frac {4}{311} \int \frac {x^2 \log (625-x) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-3+x) (5+x+4 \log (625-x))} \, dx-\frac {7518 \int \frac {x \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-625+x) (5+x+4 \log (625-x))} \, dx}{194375}-\frac {7524 \int \frac {x \log (625-x) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-625+x) (5+x+4 \log (625-x))} \, dx}{194375}+\frac {24}{311} \int \frac {\log (625-x) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-625+x) (5+x+4 \log (625-x))} \, dx+\frac {30}{311} \int \frac {\log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-625+x) (5+x+4 \log (625-x))} \, dx+\frac {414}{311} \int \frac {x^2 \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-3+x) (5+x+4 \log (625-x))} \, dx+\frac {2506}{311} \int \frac {x \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-3+x) (5+x+4 \log (625-x))} \, dx+\frac {2508}{311} \int \frac {x \log (625-x) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-3+x) (5+x+4 \log (625-x))} \, dx-\frac {5000}{311} \int \frac {\log (625-x) \log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-3+x) (5+x+4 \log (625-x))} \, dx-\frac {6250}{311} \int \frac {\log \left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right )}{(-3+x) (5+x+4 \log (625-x))} \, dx \\ & = \text {Too large to display} \\ \end{align*}
Time = 0.37 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00 \[ \int \frac {\left (37500-15036 x-2484 x^2+4 x^3+\left (30000-15048 x+24 x^2\right ) \log (625-x)\right ) \log \left (\frac {-30 x^2+10 x^3}{5+x+4 \log (625-x)}\right )}{9375 x-1265 x^2-623 x^3+x^4+\left (7500 x-2512 x^2+4 x^3\right ) \log (625-x)} \, dx=\log ^2\left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(59\) vs. \(2(24)=48\).
Time = 1.09 (sec) , antiderivative size = 60, normalized size of antiderivative = 2.50
method | result | size |
default | \(4 \ln \left (10\right ) \left (\frac {\ln \left (-x +3\right )}{2}-\frac {\ln \left (4 \ln \left (-x +625\right )+5+x \right )}{2}+\ln \left (-x \right )\right )+\ln \left (\frac {x^{2} \left (-x +3\right )}{-4 \ln \left (-x +625\right )-5-x}\right )^{2}\) | \(60\) |
risch | \(\text {Expression too large to display}\) | \(1445\) |
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Time = 0.25 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.12 \[ \int \frac {\left (37500-15036 x-2484 x^2+4 x^3+\left (30000-15048 x+24 x^2\right ) \log (625-x)\right ) \log \left (\frac {-30 x^2+10 x^3}{5+x+4 \log (625-x)}\right )}{9375 x-1265 x^2-623 x^3+x^4+\left (7500 x-2512 x^2+4 x^3\right ) \log (625-x)} \, dx=\log \left (\frac {10 \, {\left (x^{3} - 3 \, x^{2}\right )}}{x + 4 \, \log \left (-x + 625\right ) + 5}\right )^{2} \]
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Time = 0.27 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.92 \[ \int \frac {\left (37500-15036 x-2484 x^2+4 x^3+\left (30000-15048 x+24 x^2\right ) \log (625-x)\right ) \log \left (\frac {-30 x^2+10 x^3}{5+x+4 \log (625-x)}\right )}{9375 x-1265 x^2-623 x^3+x^4+\left (7500 x-2512 x^2+4 x^3\right ) \log (625-x)} \, dx=\log {\left (\frac {10 x^{3} - 30 x^{2}}{x + 4 \log {\left (625 - x \right )} + 5} \right )}^{2} \]
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Leaf count of result is larger than twice the leaf count of optimal. 125 vs. \(2 (24) = 48\).
Time = 0.34 (sec) , antiderivative size = 125, normalized size of antiderivative = 5.21 \[ \int \frac {\left (37500-15036 x-2484 x^2+4 x^3+\left (30000-15048 x+24 x^2\right ) \log (625-x)\right ) \log \left (\frac {-30 x^2+10 x^3}{5+x+4 \log (625-x)}\right )}{9375 x-1265 x^2-623 x^3+x^4+\left (7500 x-2512 x^2+4 x^3\right ) \log (625-x)} \, dx=2 \, {\left (2 \, \log \left (2\right ) + \log \left (x - 3\right ) + 2 \, \log \left (x\right )\right )} \log \left (x + 4 \, \log \left (-x + 625\right ) + 5\right ) - \log \left (x + 4 \, \log \left (-x + 625\right ) + 5\right )^{2} - 4 \, {\left (\log \left (2\right ) + \log \left (x\right )\right )} \log \left (x - 3\right ) - \log \left (x - 3\right )^{2} - 8 \, \log \left (2\right ) \log \left (x\right ) - 4 \, \log \left (x\right )^{2} + 2 \, {\left (\log \left (x - 3\right ) + 2 \, \log \left (x\right ) - \log \left (\frac {1}{4} \, x + \log \left (-x + 625\right ) + \frac {5}{4}\right )\right )} \log \left (\frac {10 \, {\left (x^{3} - 3 \, x^{2}\right )}}{x + 4 \, \log \left (-x + 625\right ) + 5}\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 129 vs. \(2 (24) = 48\).
Time = 0.32 (sec) , antiderivative size = 129, normalized size of antiderivative = 5.38 \[ \int \frac {\left (37500-15036 x-2484 x^2+4 x^3+\left (30000-15048 x+24 x^2\right ) \log (625-x)\right ) \log \left (\frac {-30 x^2+10 x^3}{5+x+4 \log (625-x)}\right )}{9375 x-1265 x^2-623 x^3+x^4+\left (7500 x-2512 x^2+4 x^3\right ) \log (625-x)} \, dx=2 \, {\left (\log \left (x - 3\right ) + 2 \, \log \left (x\right ) - \log \left (-x - 4 \, \log \left (-x + 625\right ) - 5\right )\right )} \log \left (10 \, x^{3} - 30 \, x^{2}\right ) - 2 \, {\left (\log \left (x - 3\right ) + 2 \, \log \left (x\right )\right )} \log \left (x + 4 \, \log \left (-x + 625\right ) + 5\right ) + \log \left (x + 4 \, \log \left (-x + 625\right ) + 5\right )^{2} - 2 \, {\left (\log \left (x - 3\right ) + 2 \, \log \left (x\right )\right )} \log \left (x - 3\right ) + \log \left (x - 3\right )^{2} - 4 \, \log \left (x\right )^{2} + 2 \, {\left (\log \left (x - 3\right ) + 2 \, \log \left (x\right )\right )} \log \left (-x - 4 \, \log \left (-x + 625\right ) - 5\right ) \]
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Time = 9.44 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.21 \[ \int \frac {\left (37500-15036 x-2484 x^2+4 x^3+\left (30000-15048 x+24 x^2\right ) \log (625-x)\right ) \log \left (\frac {-30 x^2+10 x^3}{5+x+4 \log (625-x)}\right )}{9375 x-1265 x^2-623 x^3+x^4+\left (7500 x-2512 x^2+4 x^3\right ) \log (625-x)} \, dx={\ln \left (-\frac {30\,x^2-10\,x^3}{x+4\,\ln \left (625-x\right )+5}\right )}^2 \]
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