\[ \int \frac {-320+480 x^2+320 x^3+60 x^4+e^{\frac {4}{5} (40+3 x)} (-20+48 x)+e^{\frac {3}{5} (40+3 x)} \left (160-288 x-144 x^2\right )+e^{\frac {2}{5} (40+3 x)} \left (-480+576 x+696 x^2+144 x^3\right )+e^{\frac {1}{5} (40+3 x)} \left (640-384 x-1056 x^2-448 x^3-48 x^4\right )+\left (160 x+10 e^{\frac {4}{5} (40+3 x)} x+320 x^2+240 x^3+80 x^4+10 x^5+e^{\frac {3}{5} (40+3 x)} \left (-80 x-40 x^2\right )+e^{\frac {2}{5} (40+3 x)} \left (240 x+240 x^2+60 x^3\right )+e^{\frac {1}{5} (40+3 x)} \left (-320 x-480 x^2-240 x^3-40 x^4\right )\right ) \log (x)+\left (160 x^2+12 e^{\frac {4}{5} (40+3 x)} x^2+240 x^3+120 x^4+20 x^5+e^{\frac {3}{5} (40+3 x)} \left (-92 x^2-36 x^3\right )+e^{\frac {2}{5} (40+3 x)} \left (264 x^2+204 x^3+36 x^4\right )+e^{\frac {1}{5} (40+3 x)} \left (-336 x^2-384 x^3-132 x^4-12 x^5\right )\right ) \log ^2(x)}{5 x^2} \, dx \]
Optimal antiderivative \[ \left (2-{\mathrm e}^{\frac {3 x}{5}+8}+x \right )^{4} \left (\ln \left (x \right )^{2}+\frac {4}{x}\right ) \]
command
integrate(1/5*((12*x^2*exp(3/5*x+8)^4+(-36*x^3-92*x^2)*exp(3/5*x+8)^3+(36*x^4+204*x^3+264*x^2)*exp(3/5*x+8)^2+(-12*x^5-132*x^4-384*x^3-336*x^2)*exp(3/5*x+8)+20*x^5+120*x^4+240*x^3+160*x^2)*log(x)^2+(10*x*exp(3/5*x+8)^4+(-40*x^2-80*x)*exp(3/5*x+8)^3+(60*x^3+240*x^2+240*x)*exp(3/5*x+8)^2+(-40*x^4-240*x^3-480*x^2-320*x)*exp(3/5*x+8)+10*x^5+80*x^4+240*x^3+320*x^2+160*x)*log(x)+(48*x-20)*exp(3/5*x+8)^4+(-144*x^2-288*x+160)*exp(3/5*x+8)^3+(144*x^3+696*x^2+576*x-480)*exp(3/5*x+8)^2+(-48*x^4-448*x^3-1056*x^2-384*x+640)*exp(3/5*x+8)+60*x^4+320*x^3+480*x^2-320)/x^2,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {output too large to display} \]
Giac 1.7.0 via sagemath 9.3 output \[ \text {Timed out} \]_______________________________________________________