Setting values for
$b$ and
$h$ results in warnings that the integration doesn't converge on
$(0,\infty)$. Here's an example:
Integrate[Sinh[x]/((Cosh[x] + Cosh[b])*(h^2 - x^2)) /. {h -> 1, b -> 1}, {x, 0, \[Infinity]}]
Integrate::idiv: Integral of -(Sinh[x]/((-1+x^2) (Cosh[1]+Cosh[x])))
does not converge on {0,[Infinity]}.
Do you have some reason to think the integral exists for either specific values of
$h$ and
$b$ or on a different interval?
