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Thread: How to solve this improper integral involving hyperbolic functions?

  1. #1
    Senior Member Vinod's Avatar
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    How to solve this improper integral involving hyperbolic functions?

    Hello,

    I want to solve this question $\displaystyle\int_0^\infty \frac{\cos{(ax)}}{\cosh{(b)}+\cosh{(x)}} dx$ where a is real and b>0.

    I put this question in online integral calculator and WolframAlpha computational intelligence, But both of these calculators couldn't understand my problem.

    If any member of MHF knows answer to this question, he may reply with correct answer.
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  2. #2
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    Re: How to solve this improper integral involving hyperbolic functions?

    Quote Originally Posted by Vinod View Post
    Hello,

    I want to solve this question $\displaystyle\int_0^\infty \frac{\cos{(ax)}}{\cosh{(b)}+\cosh{(x)}} dx$ where a is real and b>0.

    I put this question in online integral calculator and WolframAlpha computational intelligence, But both of these calculators couldn't understand my problem.

    If any member of MHF knows answer to this question, he may reply with correct answer.
    Are you SURE it converges on both ends?
    Might try smaller pieces, [0,5], [5,10], etc.
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  3. #3
    Senior Member Vinod's Avatar
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    Re: How to solve this improper integral involving hyperbolic functions?

    Quote Originally Posted by TKHunny View Post
    Are you SURE it converges on both ends?
    Might try smaller pieces, [0,5], [5,10], etc.
    Hello,

    I think this integral cannot be solved without using contour integration.
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