Integrand size = 99, antiderivative size = 24 \[ \int \frac {\left (37500-15036 x-2484 x^2+4 x^3+\left (30000-15048 x+24 x^2\right ) \log (625-x)\right ) \log \left (\frac {-30 x^2+10 x^3}{5+x+4 \log (625-x)}\right )}{9375 x-1265 x^2-623 x^3+x^4+\left (7500 x-2512 x^2+4 x^3\right ) \log (625-x)} \, dx=\log ^2\left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right ) \] Output:
ln(10*x^2*(-3+x)/(4*ln(-x+625)+5+x))^2
Time = 0.27 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00 \[ \int \frac {\left (37500-15036 x-2484 x^2+4 x^3+\left (30000-15048 x+24 x^2\right ) \log (625-x)\right ) \log \left (\frac {-30 x^2+10 x^3}{5+x+4 \log (625-x)}\right )}{9375 x-1265 x^2-623 x^3+x^4+\left (7500 x-2512 x^2+4 x^3\right ) \log (625-x)} \, dx=\log ^2\left (\frac {10 (-3+x) x^2}{5+x+4 \log (625-x)}\right ) \] Input:
Integrate[((37500 - 15036*x - 2484*x^2 + 4*x^3 + (30000 - 15048*x + 24*x^2 )*Log[625 - x])*Log[(-30*x^2 + 10*x^3)/(5 + x + 4*Log[625 - x])])/(9375*x - 1265*x^2 - 623*x^3 + x^4 + (7500*x - 2512*x^2 + 4*x^3)*Log[625 - x]),x]
Output:
Log[(10*(-3 + x)*x^2)/(5 + x + 4*Log[625 - x])]^2
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {\left (4 x^3-2484 x^2+\left (24 x^2-15048 x+30000\right ) \log (625-x)-15036 x+37500\right ) \log \left (\frac {10 x^3-30 x^2}{x+4 \log (625-x)+5}\right )}{x^4-623 x^3-1265 x^2+\left (4 x^3-2512 x^2+7500 x\right ) \log (625-x)+9375 x} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (4 x^3-2484 x^2+\left (24 x^2-15048 x+30000\right ) \log (625-x)-15036 x+37500\right ) \log \left (\frac {x^2 (10 x-30)}{x+4 \log (625-x)+5}\right )}{x \left (x^2-628 x+1875\right ) (x+4 \log (625-x)+5)}dx\) |
| \(\Big \downarrow \) 7279 |
| \(\displaystyle \int \left (\frac {2 \left (x^3-621 x^2+6 x^2 \log (625-x)-3759 x-3762 x \log (625-x)+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{194375 (x-625) (x+4 \log (625-x)+5)}-\frac {2 \left (x^3-621 x^2+6 x^2 \log (625-x)-3759 x-3762 x \log (625-x)+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{933 (x-3) (x+4 \log (625-x)+5)}+\frac {4 \left (x^3-621 x^2+6 x^2 \log (625-x)-3759 x-3762 x \log (625-x)+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{1875 x (x+4 \log (625-x)+5)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {4 \left (x^3-621 x^2+6 \left (x^2-627 x+1250\right ) \log (625-x)-3759 x+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{(3-x) (625-x) x (x+4 \log (625-x)+5)}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 4 \int \frac {\left (x^3-621 x^2-3759 x+6 \left (x^2-627 x+1250\right ) \log (625-x)+9375\right ) \log \left (-\frac {10 (3-x) x^2}{x+4 \log (625-x)+5}\right )}{(3-x) (625-x) x (x+4 \log (625-x)+5)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 \int \left (\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{388750 (x-625) (x+4 \log (625-x)+5)}-\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{1866 (x-3) (x+4 \log (625-x)+5)}+\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{1875 x (x+4 \log (625-x)+5)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 \int \frac {\left (x^3-621 x^2-3759 x+6 \left (x^2-627 x+1250\right ) \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{(3-x) (625-x) x (x+4 \log (625-x)+5)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 \int \left (\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{388750 (x-625) (x+4 \log (625-x)+5)}-\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{1866 (x-3) (x+4 \log (625-x)+5)}+\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{1875 x (x+4 \log (625-x)+5)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 \int \frac {\left (x^3-621 x^2-3759 x+6 \left (x^2-627 x+1250\right ) \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{(3-x) (625-x) x (x+4 \log (625-x)+5)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 \int \left (\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{388750 (x-625) (x+4 \log (625-x)+5)}-\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{1866 (x-3) (x+4 \log (625-x)+5)}+\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{1875 x (x+4 \log (625-x)+5)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 \int \frac {\left (x^3-621 x^2-3759 x+6 \left (x^2-627 x+1250\right ) \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{(3-x) (625-x) x (x+4 \log (625-x)+5)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 \int \left (\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{388750 (x-625) (x+4 \log (625-x)+5)}-\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{1866 (x-3) (x+4 \log (625-x)+5)}+\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{1875 x (x+4 \log (625-x)+5)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 \int \frac {\left (x^3-621 x^2-3759 x+6 \left (x^2-627 x+1250\right ) \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{(3-x) (625-x) x (x+4 \log (625-x)+5)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 \int \left (\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{388750 (x-625) (x+4 \log (625-x)+5)}-\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{1866 (x-3) (x+4 \log (625-x)+5)}+\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{1875 x (x+4 \log (625-x)+5)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 \int \frac {\left (x^3-621 x^2-3759 x+6 \left (x^2-627 x+1250\right ) \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{(3-x) (625-x) x (x+4 \log (625-x)+5)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 \int \left (\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{388750 (x-625) (x+4 \log (625-x)+5)}-\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{1866 (x-3) (x+4 \log (625-x)+5)}+\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{1875 x (x+4 \log (625-x)+5)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 \int \frac {\left (x^3-621 x^2-3759 x+6 \left (x^2-627 x+1250\right ) \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{(3-x) (625-x) x (x+4 \log (625-x)+5)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 \int \left (\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{388750 (x-625) (x+4 \log (625-x)+5)}-\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{1866 (x-3) (x+4 \log (625-x)+5)}+\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{1875 x (x+4 \log (625-x)+5)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 \int \frac {\left (x^3-621 x^2-3759 x+6 \left (x^2-627 x+1250\right ) \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{(3-x) (625-x) x (x+4 \log (625-x)+5)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 \int \left (\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{388750 (x-625) (x+4 \log (625-x)+5)}-\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{1866 (x-3) (x+4 \log (625-x)+5)}+\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{1875 x (x+4 \log (625-x)+5)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 \int \frac {\left (x^3-621 x^2-3759 x+6 \left (x^2-627 x+1250\right ) \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{(3-x) (625-x) x (x+4 \log (625-x)+5)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 \int \left (\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{388750 (x-625) (x+4 \log (625-x)+5)}-\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{1866 (x-3) (x+4 \log (625-x)+5)}+\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{1875 x (x+4 \log (625-x)+5)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 \int \frac {\left (x^3-621 x^2-3759 x+6 \left (x^2-627 x+1250\right ) \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{(3-x) (625-x) x (x+4 \log (625-x)+5)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 \int \left (\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{388750 (x-625) (x+4 \log (625-x)+5)}-\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{1866 (x-3) (x+4 \log (625-x)+5)}+\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{1875 x (x+4 \log (625-x)+5)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 \int \frac {\left (x^3-621 x^2-3759 x+6 \left (x^2-627 x+1250\right ) \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{(3-x) (625-x) x (x+4 \log (625-x)+5)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 \int \left (\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{388750 (x-625) (x+4 \log (625-x)+5)}-\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{1866 (x-3) (x+4 \log (625-x)+5)}+\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{1875 x (x+4 \log (625-x)+5)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 \int \frac {\left (x^3-621 x^2-3759 x+6 \left (x^2-627 x+1250\right ) \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{(3-x) (625-x) x (x+4 \log (625-x)+5)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 \int \left (\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{388750 (x-625) (x+4 \log (625-x)+5)}-\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{1866 (x-3) (x+4 \log (625-x)+5)}+\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{1875 x (x+4 \log (625-x)+5)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 \int \frac {\left (x^3-621 x^2-3759 x+6 \left (x^2-627 x+1250\right ) \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{(3-x) (625-x) x (x+4 \log (625-x)+5)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 \int \left (\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{388750 (x-625) (x+4 \log (625-x)+5)}-\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{1866 (x-3) (x+4 \log (625-x)+5)}+\frac {\left (x^3+6 \log (625-x) x^2-621 x^2-3762 \log (625-x) x-3759 x+7500 \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{1875 x (x+4 \log (625-x)+5)}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 \int \frac {\left (x^3-621 x^2-3759 x+6 \left (x^2-627 x+1250\right ) \log (625-x)+9375\right ) \log \left (\frac {10 (x-3) x^2}{x+4 \log (625-x)+5}\right )}{(3-x) (625-x) x (x+4 \log (625-x)+5)}dx\) |
Input:
Int[((37500 - 15036*x - 2484*x^2 + 4*x^3 + (30000 - 15048*x + 24*x^2)*Log[ 625 - x])*Log[(-30*x^2 + 10*x^3)/(5 + x + 4*Log[625 - x])])/(9375*x - 1265 *x^2 - 623*x^3 + x^4 + (7500*x - 2512*x^2 + 4*x^3)*Log[625 - x]),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(59\) vs. \(2(24)=48\).
Time = 3.88 (sec) , antiderivative size = 60, normalized size of antiderivative = 2.50
| method | result | size |
| default | \(4 \ln \left (10\right ) \left (\frac {\ln \left (-x +3\right )}{2}-\frac {\ln \left (4 \ln \left (-x +625\right )+5+x \right )}{2}+\ln \left (-x \right )\right )+\ln \left (\frac {x^{2} \left (-x +3\right )}{-x -5-4 \ln \left (-x +625\right )}\right )^{2}\) | \(60\) |
| risch | \(\text {Expression too large to display}\) | \(1445\) |
Input:
int(((24*x^2-15048*x+30000)*ln(-x+625)+4*x^3-2484*x^2-15036*x+37500)*ln((1 0*x^3-30*x^2)/(4*ln(-x+625)+5+x))/((4*x^3-2512*x^2+7500*x)*ln(-x+625)+x^4- 623*x^3-1265*x^2+9375*x),x,method=_RETURNVERBOSE)
Output:
4*ln(10)*(1/2*ln(-x+3)-1/2*ln(4*ln(-x+625)+5+x)+ln(-x))+ln(x^2*(-x+3)/(-x- 5-4*ln(-x+625)))^2
Time = 0.07 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.12 \[ \int \frac {\left (37500-15036 x-2484 x^2+4 x^3+\left (30000-15048 x+24 x^2\right ) \log (625-x)\right ) \log \left (\frac {-30 x^2+10 x^3}{5+x+4 \log (625-x)}\right )}{9375 x-1265 x^2-623 x^3+x^4+\left (7500 x-2512 x^2+4 x^3\right ) \log (625-x)} \, dx=\log \left (\frac {10 \, {\left (x^{3} - 3 \, x^{2}\right )}}{x + 4 \, \log \left (-x + 625\right ) + 5}\right )^{2} \] Input:
integrate(((24*x^2-15048*x+30000)*log(-x+625)+4*x^3-2484*x^2-15036*x+37500 )*log((10*x^3-30*x^2)/(4*log(-x+625)+5+x))/((4*x^3-2512*x^2+7500*x)*log(-x +625)+x^4-623*x^3-1265*x^2+9375*x),x, algorithm="fricas")
Output:
log(10*(x^3 - 3*x^2)/(x + 4*log(-x + 625) + 5))^2
Time = 0.30 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.92 \[ \int \frac {\left (37500-15036 x-2484 x^2+4 x^3+\left (30000-15048 x+24 x^2\right ) \log (625-x)\right ) \log \left (\frac {-30 x^2+10 x^3}{5+x+4 \log (625-x)}\right )}{9375 x-1265 x^2-623 x^3+x^4+\left (7500 x-2512 x^2+4 x^3\right ) \log (625-x)} \, dx=\log {\left (\frac {10 x^{3} - 30 x^{2}}{x + 4 \log {\left (625 - x \right )} + 5} \right )}^{2} \] Input:
integrate(((24*x**2-15048*x+30000)*ln(-x+625)+4*x**3-2484*x**2-15036*x+375 00)*ln((10*x**3-30*x**2)/(4*ln(-x+625)+5+x))/((4*x**3-2512*x**2+7500*x)*ln (-x+625)+x**4-623*x**3-1265*x**2+9375*x),x)
Output:
log((10*x**3 - 30*x**2)/(x + 4*log(625 - x) + 5))**2
Leaf count of result is larger than twice the leaf count of optimal. 125 vs. \(2 (24) = 48\).
Time = 0.17 (sec) , antiderivative size = 125, normalized size of antiderivative = 5.21 \[ \int \frac {\left (37500-15036 x-2484 x^2+4 x^3+\left (30000-15048 x+24 x^2\right ) \log (625-x)\right ) \log \left (\frac {-30 x^2+10 x^3}{5+x+4 \log (625-x)}\right )}{9375 x-1265 x^2-623 x^3+x^4+\left (7500 x-2512 x^2+4 x^3\right ) \log (625-x)} \, dx=2 \, {\left (2 \, \log \left (2\right ) + \log \left (x - 3\right ) + 2 \, \log \left (x\right )\right )} \log \left (x + 4 \, \log \left (-x + 625\right ) + 5\right ) - \log \left (x + 4 \, \log \left (-x + 625\right ) + 5\right )^{2} - 4 \, {\left (\log \left (2\right ) + \log \left (x\right )\right )} \log \left (x - 3\right ) - \log \left (x - 3\right )^{2} - 8 \, \log \left (2\right ) \log \left (x\right ) - 4 \, \log \left (x\right )^{2} + 2 \, {\left (\log \left (x - 3\right ) + 2 \, \log \left (x\right ) - \log \left (\frac {1}{4} \, x + \log \left (-x + 625\right ) + \frac {5}{4}\right )\right )} \log \left (\frac {10 \, {\left (x^{3} - 3 \, x^{2}\right )}}{x + 4 \, \log \left (-x + 625\right ) + 5}\right ) \] Input:
integrate(((24*x^2-15048*x+30000)*log(-x+625)+4*x^3-2484*x^2-15036*x+37500 )*log((10*x^3-30*x^2)/(4*log(-x+625)+5+x))/((4*x^3-2512*x^2+7500*x)*log(-x +625)+x^4-623*x^3-1265*x^2+9375*x),x, algorithm="maxima")
Output:
2*(2*log(2) + log(x - 3) + 2*log(x))*log(x + 4*log(-x + 625) + 5) - log(x + 4*log(-x + 625) + 5)^2 - 4*(log(2) + log(x))*log(x - 3) - log(x - 3)^2 - 8*log(2)*log(x) - 4*log(x)^2 + 2*(log(x - 3) + 2*log(x) - log(1/4*x + log (-x + 625) + 5/4))*log(10*(x^3 - 3*x^2)/(x + 4*log(-x + 625) + 5))
Leaf count of result is larger than twice the leaf count of optimal. 129 vs. \(2 (24) = 48\).
Time = 0.15 (sec) , antiderivative size = 129, normalized size of antiderivative = 5.38 \[ \int \frac {\left (37500-15036 x-2484 x^2+4 x^3+\left (30000-15048 x+24 x^2\right ) \log (625-x)\right ) \log \left (\frac {-30 x^2+10 x^3}{5+x+4 \log (625-x)}\right )}{9375 x-1265 x^2-623 x^3+x^4+\left (7500 x-2512 x^2+4 x^3\right ) \log (625-x)} \, dx=2 \, {\left (\log \left (x - 3\right ) + 2 \, \log \left (x\right ) - \log \left (-x - 4 \, \log \left (-x + 625\right ) - 5\right )\right )} \log \left (10 \, x^{3} - 30 \, x^{2}\right ) - 2 \, {\left (\log \left (x - 3\right ) + 2 \, \log \left (x\right )\right )} \log \left (x + 4 \, \log \left (-x + 625\right ) + 5\right ) + \log \left (x + 4 \, \log \left (-x + 625\right ) + 5\right )^{2} - 2 \, {\left (\log \left (x - 3\right ) + 2 \, \log \left (x\right )\right )} \log \left (x - 3\right ) + \log \left (x - 3\right )^{2} - 4 \, \log \left (x\right )^{2} + 2 \, {\left (\log \left (x - 3\right ) + 2 \, \log \left (x\right )\right )} \log \left (-x - 4 \, \log \left (-x + 625\right ) - 5\right ) \] Input:
integrate(((24*x^2-15048*x+30000)*log(-x+625)+4*x^3-2484*x^2-15036*x+37500 )*log((10*x^3-30*x^2)/(4*log(-x+625)+5+x))/((4*x^3-2512*x^2+7500*x)*log(-x +625)+x^4-623*x^3-1265*x^2+9375*x),x, algorithm="giac")
Output:
2*(log(x - 3) + 2*log(x) - log(-x - 4*log(-x + 625) - 5))*log(10*x^3 - 30* x^2) - 2*(log(x - 3) + 2*log(x))*log(x + 4*log(-x + 625) + 5) + log(x + 4* log(-x + 625) + 5)^2 - 2*(log(x - 3) + 2*log(x))*log(x - 3) + log(x - 3)^2 - 4*log(x)^2 + 2*(log(x - 3) + 2*log(x))*log(-x - 4*log(-x + 625) - 5)
Time = 1.30 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.21 \[ \int \frac {\left (37500-15036 x-2484 x^2+4 x^3+\left (30000-15048 x+24 x^2\right ) \log (625-x)\right ) \log \left (\frac {-30 x^2+10 x^3}{5+x+4 \log (625-x)}\right )}{9375 x-1265 x^2-623 x^3+x^4+\left (7500 x-2512 x^2+4 x^3\right ) \log (625-x)} \, dx={\ln \left (-\frac {30\,x^2-10\,x^3}{x+4\,\ln \left (625-x\right )+5}\right )}^2 \] Input:
int((log(-(30*x^2 - 10*x^3)/(x + 4*log(625 - x) + 5))*(log(625 - x)*(24*x^ 2 - 15048*x + 30000) - 15036*x - 2484*x^2 + 4*x^3 + 37500))/(9375*x + log( 625 - x)*(7500*x - 2512*x^2 + 4*x^3) - 1265*x^2 - 623*x^3 + x^4),x)
Output:
log(-(30*x^2 - 10*x^3)/(x + 4*log(625 - x) + 5))^2
Time = 0.25 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.17 \[ \int \frac {\left (37500-15036 x-2484 x^2+4 x^3+\left (30000-15048 x+24 x^2\right ) \log (625-x)\right ) \log \left (\frac {-30 x^2+10 x^3}{5+x+4 \log (625-x)}\right )}{9375 x-1265 x^2-623 x^3+x^4+\left (7500 x-2512 x^2+4 x^3\right ) \log (625-x)} \, dx=\mathrm {log}\left (\frac {10 x^{3}-30 x^{2}}{4 \,\mathrm {log}\left (-x +625\right )+x +5}\right )^{2} \] Input:
int(((24*x^2-15048*x+30000)*log(-x+625)+4*x^3-2484*x^2-15036*x+37500)*log( (10*x^3-30*x^2)/(4*log(-x+625)+5+x))/((4*x^3-2512*x^2+7500*x)*log(-x+625)+ x^4-623*x^3-1265*x^2+9375*x),x)
Output:
log((10*x**3 - 30*x**2)/(4*log( - x + 625) + x + 5))**2