I am trying to find the integration of the following
$$\int_0^\infty {\frac{{\ln \left( {1 + x} \right)}}{{1 + ax}}{e^{ - bx}}{x^n}{\rm{d}}x} $$
Here $a>0, b>0$, and $n$ is an integer.
I think if we get the Meijer-G representation of
$$\frac{{\ln \left( {1 + x} \right)}}{{1 + ax}}$$
we can use Laplace transform to get the closed-form expression. But I don't know how to express the above function as Meijer-G function.
Thanks.