\[ \int \frac {10+10 e^{4 x/5}+e^{3 x/5} (40-40 x)-40 x+60 x^2-40 x^3+10 x^4+e^{2 x/5} \left (60-120 x+60 x^2\right )+e^{x/5} \left (40-120 x+120 x^2-40 x^3\right )+\left (10+60 x^2-80 x^3+30 x^4+e^{4 x/5} (-10+8 x)+e^{3 x/5} \left (-40+24 x-24 x^2\right )+e^{2 x/5} \left (-60+24 x+12 x^2+24 x^3\right )+e^{x/5} \left (-40+8 x+96 x^2-56 x^3-8 x^4\right )\right ) \log (x)-10 \log ^2(x)}{5 x^2} \, dx \]
Optimal antiderivative \[ \frac {2 \left (\ln \left (x \right )+\left (x -{\mathrm e}^{\frac {x}{5}}-1\right )^{4}\right ) \ln \left (x \right )}{x} \]
command
integrate(1/5*(-10*log(x)^2+((8*x-10)*exp(1/5*x)^4+(-24*x^2+24*x-40)*exp(1/5*x)^3+(24*x^3+12*x^2+24*x-60)*exp(1/5*x)^2+(-8*x^4-56*x^3+96*x^2+8*x-40)*exp(1/5*x)+30*x^4-80*x^3+60*x^2+10)*log(x)+10*exp(1/5*x)^4+(-40*x+40)*exp(1/5*x)^3+(60*x^2-120*x+60)*exp(1/5*x)^2+(-40*x^3+120*x^2-120*x+40)*exp(1/5*x)+10*x^4-40*x^3+60*x^2-40*x+10)/x^2,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {2 \, {\left (x^{4} \log \left (5\right ) - 4 \, x^{3} e^{\left (\frac {1}{5} \, x\right )} \log \left (5\right ) + x^{4} \log \left (\frac {1}{5} \, x\right ) - 4 \, x^{3} e^{\left (\frac {1}{5} \, x\right )} \log \left (\frac {1}{5} \, x\right ) - 4 \, x^{3} \log \left (5\right ) + 6 \, x^{2} e^{\left (\frac {2}{5} \, x\right )} \log \left (5\right ) + 12 \, x^{2} e^{\left (\frac {1}{5} \, x\right )} \log \left (5\right ) - 4 \, x^{3} \log \left (\frac {1}{5} \, x\right ) + 6 \, x^{2} e^{\left (\frac {2}{5} \, x\right )} \log \left (\frac {1}{5} \, x\right ) + 12 \, x^{2} e^{\left (\frac {1}{5} \, x\right )} \log \left (\frac {1}{5} \, x\right ) + 6 \, x^{2} \log \left (5\right ) - 4 \, x e^{\left (\frac {3}{5} \, x\right )} \log \left (5\right ) - 12 \, x e^{\left (\frac {2}{5} \, x\right )} \log \left (5\right ) - 12 \, x e^{\left (\frac {1}{5} \, x\right )} \log \left (5\right ) + 6 \, x^{2} \log \left (\frac {1}{5} \, x\right ) - 4 \, x e^{\left (\frac {3}{5} \, x\right )} \log \left (\frac {1}{5} \, x\right ) - 12 \, x e^{\left (\frac {2}{5} \, x\right )} \log \left (\frac {1}{5} \, x\right ) - 12 \, x e^{\left (\frac {1}{5} \, x\right )} \log \left (\frac {1}{5} \, x\right ) + e^{\left (\frac {4}{5} \, x\right )} \log \left (5\right ) + 4 \, e^{\left (\frac {3}{5} \, x\right )} \log \left (5\right ) + 6 \, e^{\left (\frac {2}{5} \, x\right )} \log \left (5\right ) + 4 \, e^{\left (\frac {1}{5} \, x\right )} \log \left (5\right ) + \log \left (5\right )^{2} - 4 \, x \log \left (\frac {1}{5} \, x\right ) + e^{\left (\frac {4}{5} \, x\right )} \log \left (\frac {1}{5} \, x\right ) + 4 \, e^{\left (\frac {3}{5} \, x\right )} \log \left (\frac {1}{5} \, x\right ) + 6 \, e^{\left (\frac {2}{5} \, x\right )} \log \left (\frac {1}{5} \, x\right ) + 4 \, e^{\left (\frac {1}{5} \, x\right )} \log \left (\frac {1}{5} \, x\right ) + 2 \, \log \left (5\right ) \log \left (\frac {1}{5} \, x\right ) + \log \left (\frac {1}{5} \, x\right )^{2} + \log \left (5\right ) + \log \left (\frac {1}{5} \, x\right )\right )}}{x} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________