How to solve the following definite integral:
$$\int\limits_0^\infty {\gamma \left( {N,\frac{c}{{ax + b}}} \right){e^{ - x}}dx} $$?
$a, b, c \in \mathbb{R}$ and $a,b,c>0$ This is indeed similar to the CDF for the product of a gamma-distributed variable and an exponential-distributed variable, but they are different due to $b$. I can't find the closed-form solution or approximate solution of the above definite integral.