43.53 Problem number 7789

$$\int x^{35+609x+2650x^2+625x^3+e^2(4+x)}(72+1218x+5300x^2+1250x^3+e^2(8+2x)+(1218x+2e^{2}x+10600x^2+3750x^3)\log (x))dx$$

Optimal antiderivative $$2{\mathrm{e}}^{({(3+25x)}^2+{\mathrm{e}}^2)(4+x)\ln \left(x\right)}$$

command

integrate(((2*exp(2)*x+3750*x^3+10600*x^2+1218*x)*log(x)+(2*x+8)*exp(2)+1250*x^3+5300*x^2+1218*x+72)*exp(((4+x)*exp(2)+625*x^3+2650*x^2+609*x+36)*log(x))/x,x, algorithm="giac")

Giac 1.9.0-11 via sagemath 9.6 output

$$\text{could not integrate}$$

Giac 1.7.0 via sagemath 9.3 output

$$2e^{(625x^3\log \left(x\right)+2650x^2\log \left(x\right)+x{e}^2\log \left(x\right)+609x\log \left(x\right)+4e^2\log \left(x\right)+36\log \left(x\right))}$$