43.37 Problem number 5649

$$\int \frac{e^{\frac{-7x+e^{36+e^4+12x^2+x^4+e^2(-12-2x^2)}x}{16+\log (x)}}(-105+e^{36+e^4+12x^2+x^4+e^2(-12-2x^2)}(15+384x^2-64e^2{x}^2+64x^4)+(-7+e^{36+e^4+12x^2+x^4+e^2(-12-2x^2)}(1+24x^2-4e^2{x}^2+4x^4))\log (x))}{256+32\log (x)+{\log }^2(x)}dx$$

Optimal antiderivative $${\mathrm{e}}^{\frac{x({\mathrm{e}}^{{({\mathrm{e}}^2-x^2-6)}^2}-7)}{16+\ln \left(x\right)}}$$

command

integrate((((-4*x^2*exp(2)+4*x^4+24*x^2+1)*exp(exp(2)^2+(-2*x^2-12)*exp(2)+x^4+12*x^2+36)-7)*log(x)+(-64*x^2*exp(2)+64*x^4+384*x^2+15)*exp(exp(2)^2+(-2*x^2-12)*exp(2)+x^4+12*x^2+36)-105)*exp((x*exp(exp(2)^2+(-2*x^2-12)*exp(2)+x^4+12*x^2+36)-7*x)/(16+log(x)))/(log(x)^2+32*log(x)+256),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

$$e^{(\frac{x{e}^{(x^4-2x^2{e}^2+12x^2+e^4-12e^2+36)}}{\log \left(x\right)+16}-\frac{7x}{\log \left(x\right)+16})}$$