\[ \int \frac {x^{\frac {5 x^2}{15-8 x+6 x^2+(-8+2 x) \log (4)+\log ^2(4)}} \left (75 x-40 x^2+30 x^3+\left (-40 x+10 x^2\right ) \log (4)+5 x \log ^2(4)+\left (150 x-40 x^2+\left (-80 x+10 x^2\right ) \log (4)+10 x \log ^2(4)\right ) \log (x)\right )}{225-240 x+244 x^2-96 x^3+36 x^4+\left (-240+188 x-128 x^2+24 x^3\right ) \log (4)+\left (94-48 x+16 x^2\right ) \log ^2(4)+(-16+4 x) \log ^3(4)+\log ^4(4)} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\frac {\ln \left (x \right ) x}{\frac {\left (x -4+2 \ln \left (2\right )\right )^{2}-1}{5 x}+x}} \]
command
integrate(((40*x*log(2)^2+2*(10*x^2-80*x)*log(2)-40*x^2+150*x)*log(x)+20*x*log(2)^2+2*(10*x^2-40*x)*log(2)+30*x^3-40*x^2+75*x)*exp(5*x^2*log(x)/(4*log(2)^2+2*(2*x-8)*log(2)+6*x^2-8*x+15))/(16*log(2)^4+8*(4*x-16)*log(2)^3+4*(16*x^2-48*x+94)*log(2)^2+2*(24*x^3-128*x^2+188*x-240)*log(2)+36*x^4-96*x^3+244*x^2-240*x+225),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ x^{\frac {5 \, x^{2}}{6 \, x^{2} + 4 \, x \log \left (2\right ) + 4 \, \log \left (2\right )^{2} - 8 \, x - 16 \, \log \left (2\right ) + 15}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: TypeError} \]________________________________________________________________________________________