I am trying to solve the following integral using Mathematica,

Assuming[a > 0, Limit[Integrate[(1 - y*E^(b*y)*Gamma[0, y/b])/(1 + a*y), {y, 0, m}], m ->Infinity]]

\begin{equation}\mathop {\lim }\limits_{m \to \infty } \int_0^m {\frac{{1 - y{e^{by}}{\rm{Gamma}}\left[ {0,\frac{y}{b}} \right]}}{{1 + ay}}} dy\end{equation}

Mathematica doesn't provide any result to the integral, just shows the original equation as the output. I was trying to solve it myself, however found it too difficult to proceed further. I would be grateful if anyone could help me solving the integral.