Integral $\int_0^\infty \frac{e^{-cy} dy }{1+ay}$ $$I'=\int_0^\infty \frac{e^{-cy} dy }{1+ay}$$
a, b, and c, are positive coefficients. This integral is part of a problem which I'm trying to solve it and after lot's of effort the problem transform into two parts. For solving the second part(the question I asked you) I can't go through, unfortunately.

Hint
Let us look at the antiderivative and, first, make a change of variable $1+ay=x$. So, $$I=\int\frac{e^{-cy}}{1+ay}\,dy=\frac{e^{c/a}}{a}\int\frac{e^{-cx/a}}{x}\,dx$$ Now, change again setting $\frac{cx}{a}=z$; you then arrive to $$I=\frac{e^{c/a}}{a}\int\frac{e^{-z}}{z}\,dz=\frac{e^{c/a}}{a}\text{Ei}(-z)$$ where appears the exponential integral.
