\[ \int \frac {e^{2 \log ^2(x)} \left (64 x+32 x^2-96 x^3+\left (64 x+32 x^2-96 x^3\right ) \log (15)+\left (16 x+8 x^2-24 x^3\right ) \log ^2(15)+\left (128 x-64 x^2+64 x^3+\left (128 x-64 x^2+64 x^3\right ) \log (15)+\left (32 x-16 x^2+16 x^3\right ) \log ^2(15)\right ) \log (x)\right )}{32-80 x+160 x^2-200 x^3+210 x^4-161 x^5+105 x^6-50 x^7+20 x^8-5 x^9+x^{10}} \, dx \]
Optimal antiderivative \[ \frac {\left (4+2 \ln \! \left (15\right )\right )^{2} {\mathrm e}^{2 \ln \left (x \right )^{2}} x^{2}}{\left (x^{2}-x +2\right )^{4}} \]
command
Int[(E^(2*Log[x]^2)*(64*x + 32*x^2 - 96*x^3 + (64*x + 32*x^2 - 96*x^3)*Log[15] + (16*x + 8*x^2 - 24*x^3)*Log[15]^2 + (128*x - 64*x^2 + 64*x^3 + (128*x - 64*x^2 + 64*x^3)*Log[15] + (32*x - 16*x^2 + 16*x^3)*Log[15]^2)*Log[x]))/(32 - 80*x + 160*x^2 - 200*x^3 + 210*x^4 - 161*x^5 + 105*x^6 - 50*x^7 + 20*x^8 - 5*x^9 + x^10),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {e^{2 \log ^2(x)} \left (64 x+32 x^2-96 x^3+\left (64 x+32 x^2-96 x^3\right ) \log (15)+\left (16 x+8 x^2-24 x^3\right ) \log ^2(15)+\left (128 x-64 x^2+64 x^3+\left (128 x-64 x^2+64 x^3\right ) \log (15)+\left (32 x-16 x^2+16 x^3\right ) \log ^2(15)\right ) \log (x)\right )}{32-80 x+160 x^2-200 x^3+210 x^4-161 x^5+105 x^6-50 x^7+20 x^8-5 x^9+x^{10}} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \frac {4 x e^{2 \log ^2(x)} \left (4 x^3-4 x^2+\left (x^3-x^2+2 x\right ) \log ^2(15)+4 \left (x^3-x^2+2 x\right ) \log (15)+8 x\right )}{x^{10}-5 x^9+20 x^8-50 x^7+105 x^6-161 x^5+210 x^4-200 x^3+160 x^2-80 x+32} \]