100.96 Problem number 3906

\[ \int \frac {-18-18 e^9+36 x}{\left (8000+1200 x-1140 x^2-119 x^3+57 x^4+3 x^5-x^6+e^{27} \left (64+48 x+12 x^2+x^3\right )+e^{18} \left (960+528 x+36 x^2-21 x^3-3 x^4\right )+e^9 \left (4800+1680 x-348 x^2-141 x^3+6 x^4+3 x^5\right )\right ) \log ^2(5)} \, dx \]

Optimal antiderivative \[ \frac {9}{\ln \left (5\right )^{2} \left (4+x \right )^{2} \left (x -5-{\mathrm e}^{9}\right )^{2}} \]

command

integrate((-18*exp(9)+36*x-18)/((x^3+12*x^2+48*x+64)*exp(9)^3+(-3*x^4-21*x^3+36*x^2+528*x+960)*exp(9)^2+(3*x^5+6*x^4-141*x^3-348*x^2+1680*x+4800)*exp(9)-x^6+3*x^5+57*x^4-119*x^3-1140*x^2+1200*x+8000)/log(5)^2,x, algorithm="giac")

Giac 1.9.0-11 via sagemath 9.6 output

\[ \frac {9}{{\left (x^{2} - x e^{9} - x - 4 \, e^{9} - 20\right )}^{2} \log \left (5\right )^{2}} \]

Giac 1.7.0 via sagemath 9.3 output

\[ \text {Timed out} \]________________________________________________________________________________________