\[ \int \frac {10+13 x+7 x^2+e \left (-10-8 x+2 x^2-2 x^3\right )+\left (-2-3 x-2 x^2+e (2+2 x)\right ) \log (4)+\left (7 x+4 x^2+x^3+e \left (-2 x-4 x^2\right )-x \log (4)\right ) \log (2 x)}{200 x-80 x^2-72 x^3+16 x^4+8 x^5+\left (-80 x+16 x^2+16 x^3\right ) \log (4)+8 x \log ^2(4)} \, dx \]
Optimal antiderivative \[ \frac {\left (\ln \! \left (2 x \right )+x \right ) \left (\frac {{\mathrm e}}{4}-\frac {1}{4}-\frac {x}{8}\right )}{x^{2}+2 \ln \! \left (2\right )+x -5} \]
command
Int[(10 + 13*x + 7*x^2 + E*(-10 - 8*x + 2*x^2 - 2*x^3) + (-2 - 3*x - 2*x^2 + E*(2 + 2*x))*Log[4] + (7*x + 4*x^2 + x^3 + E*(-2*x - 4*x^2) - x*Log[4])*Log[2*x])/(200*x - 80*x^2 - 72*x^3 + 16*x^4 + 8*x^5 + (-80*x + 16*x^2 + 16*x^3)*Log[4] + 8*x*Log[4]^2),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {10+13 x+7 x^2+e \left (-10-8 x+2 x^2-2 x^3\right )+\left (-2-3 x-2 x^2+e (2+2 x)\right ) \log (4)+\left (7 x+4 x^2+x^3+e \left (-2 x-4 x^2\right )-x \log (4)\right ) \log (2 x)}{200 x-80 x^2-72 x^3+16 x^4+8 x^5+\left (-80 x+16 x^2+16 x^3\right ) \log (4)+8 x \log ^2(4)} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \text {output too large to display} \]