# Thread: a difficult integral

1. ## a difficult integral

Hello frindes i was hopeing some of you might help me with a difficult integral i am facing
$\int\frac{\coth(ax)}{\exp(bx)-\cos^2(c)}dx$
On the intervale of $[0,\infty]$, 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 $a\rightarrow\infty$ 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

2. Originally Posted by elfsong
Hello frindes i was hopeing some of you might help me with a difficult integral i am facing
$\int\frac{\coth(ax)}{\exp(bx)-\cos^2(c)}dx$
On the intervale of $[0,\infty]$, 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 $a\rightarrow\infty$ 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
My CAS could not find a solution for what you posted.

Are you sure it wasn't

$\int_0^\infty{\frac{\coth{(ax)}}{e^{(bx)}-\cos^2{(cx)}}\,dx}$?

My CAS tells me that this is undefined...

3. i am certine about the exprassion i gave, it is a reduced form of the original term
most integration sofware i used could not tell me anything about this integral...
but it should exist

if you's like i can add the original term