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Thread: Are these two integrals equal?

  1. #1
    Senior Member Vinod's Avatar
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    Are these two integrals equal?

    Hello,
    Are the following two integrals equal?

    $2\displaystyle\int_0^\infty\frac{t^a dt}{((b+1)t+(b-1))^2}=\frac{2}{b^2-1}\bigg(\frac{b-1}{b+1}\bigg)^{a+1}\displaystyle\int_0^\infty\frac {u^adu}{(u+1)^2}$ where $u=\frac{(b+1)t}{b-1}$

    If they are equal, how are they equal explaining the denominator term $b^2-1$ on the right hand side integral.
    Last edited by Vinod; Dec 21st 2018 at 08:47 AM.
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  2. #2
    Member Walagaster's Avatar
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    Re: Are these two integrals equal?

    Quote Originally Posted by Vinod View Post
    Hello,
    Are the following two integrals equal?

    $2\displaystyle\int_0^\infty\frac{t^a dt}{((b+1)t+(b-1))^2}=\frac{2}{b^2-1}\bigg(\frac{b-1}{b+1}\bigg)^{a+1}\displaystyle\int_0^\infty\frac {u^adu}{(u+1)^2}$ where $u=\frac{(b+1)t}{b-1}$

    If they are equal, how are they equal explaining the denominator term $b^2-1$ on the right hand side integral.
    I think there is a typo and that the $b^2-1$ should be $(b-1)^2$. Is that what you get?
    Thanks from topsquark
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