I would like to evaluate:
$$ \int\_{0}^{\infty} \frac{1}{\sqrt{x(1+e^x)}}\mathrm dx $$
Given that I can't find $ \int \frac{1}{\sqrt{x(1+e^x)}}\mathrm dx $, a substitution is needed: I tried $$ u=\sqrt{x(1+e^x)} $$ and $$ u=\frac{1}{\sqrt{x(1+e^x)}} $$ but I could not get rid of $x$ in the new integral....
Do you have ideas of substitution?