I split this to get
\begin{equation}
\int ^{\infty} _{0} \dfrac{e^{ax}}{(1+e^{ax})(1+e^{bx})} \ dx - \int ^{\infty} _{0} \dfrac{e^{bx}}{(1+e^{ax})(1+e^{bx})} \ dx
\end{equation}
Then I tried to solve the first term (both term are similars). The problem is that I made a substitution (many ones...