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Math Help - complex analysis question

  1. #1
    Member Mentia's Avatar
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    complex analysis question

    How would you apply complex analysis/the residue theorem to evaluate the following improper integral:

    <br />
\int_{0}^{\infty} \frac{2 t}{\left(t^{2}+1\right)^{2}} \,dt
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  2. #2
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    Quote Originally Posted by Mentia View Post
    How would you apply complex analysis/the residue theorem to evaluate the following improper integral:

    <br />
\int_{0}^{\infty} \frac{2 t}{\left(t^{2}+1\right)^{2}} \,dt
    Do you really have to pick an integral which can easily be solved with x=t^2+1?
    It it just Palinful to do an integral which solves easily with substitution.
    Is it okay with you if I do a less trivial integral such as, \int_0^{\infty} \frac{dt}{(t^2+1)^2}?
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