\[ \int \frac {e^x (-220-20 x+40 \log (2))+e^x (44+4 x) \log (2) \log (11+x)+\left (e^x \left (-220-240 x-20 x^2+\left (-44 x-48 x^2-4 x^3\right ) \log (2)\right )+e^x \left (44+48 x+4 x^2\right ) \log (2) \log (11+x)\right ) \log \left (\frac {(1+x) \log (2)}{-5-x \log (2)+\log (2) \log (11+x)}\right )}{-55-60 x-5 x^2+\left (-11 x-12 x^2-x^3\right ) \log (2)+\left (11+12 x+x^2\right ) \log (2) \log (11+x)} \, dx \]
Optimal antiderivative \[ 4 \ln \! \left (\frac {1+x}{\ln \! \left (11+x \right )-x -\frac {5}{\ln \left (2\right )}}\right ) {\mathrm e}^{x} \]
command
Int[(E^x*(-220 - 20*x + 40*Log[2]) + E^x*(44 + 4*x)*Log[2]*Log[11 + x] + (E^x*(-220 - 240*x - 20*x^2 + (-44*x - 48*x^2 - 4*x^3)*Log[2]) + E^x*(44 + 48*x + 4*x^2)*Log[2]*Log[11 + x])*Log[((1 + x)*Log[2])/(-5 - x*Log[2] + Log[2]*Log[11 + x])])/(-55 - 60*x - 5*x^2 + (-11*x - 12*x^2 - x^3)*Log[2] + (11 + 12*x + x^2)*Log[2]*Log[11 + x]),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {e^x (-220-20 x+40 \log (2))+e^x (44+4 x) \log (2) \log (11+x)+\left (e^x \left (-220-240 x-20 x^2+\left (-44 x-48 x^2-4 x^3\right ) \log (2)\right )+e^x \left (44+48 x+4 x^2\right ) \log (2) \log (11+x)\right ) \log \left (\frac {(1+x) \log (2)}{-5-x \log (2)+\log (2) \log (11+x)}\right )}{-55-60 x-5 x^2+\left (-11 x-12 x^2-x^3\right ) \log (2)+\left (11+12 x+x^2\right ) \log (2) \log (11+x)} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ 4 e^x \log \left (-\frac {(x+1) \log (2)}{x \log (2)-\log (2) \log (x+11)+5}\right ) \]