$$ I=\int_0^{+\infty} \frac{Q_1(a,\sqrt{by})}{1+cy}dy $$ $a$, $b$, and $c$ are positive coefficients. $Q_1$ is Marcum $q$-function. 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.
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This is not a definite integral but an improper one. – Timbuc Jan 26 '15 at 08:20
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@Timbuc No, it's a definite integral AND an improper one. – David H Jan 29 '15 at 10:23
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@DavidH Point taken, though I think it may depend on definition. – Timbuc Jan 29 '15 at 11:21