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Math Help - a difficult integral

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by elfsong View Post
    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...
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  3. #3
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    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
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