Hello frindes i was hopeing some of you might help me with a difficult integral i am facing

On the intervale of

, I know it's not a normal integral but I need it for a small work i am doing

the value of either a or b could be complex, c is a real parameter

I already tried using the resedium of the integral,

but it does not fit with a limit i need to take when

as that result is known to me allready.

I tried integration by parts but got nowhere fast

I need an exact solution and the value of the integral

Thank you in advence