I've been desperately trying to solve the following integral without much success. $$I(u)=\int_1^u \frac{e^{-x} (2 x-1)}{\sqrt{x~(A~e^{-x}+1)-B \sqrt{x}}}dx,$$ where $A,B\in \mathbb{R}$ are constants such that the integrand has no singularities.
Mathematica spits the integral right after I press "evaluate". Maybe this is an indication that the integral can't be solved analytically but there has been times where Mathematica can't find a solution and it indeed exists. If it has analytical solution I don't seem to have the skill to find it... Could someone please help me?
