I am trying to evaluate the following:
∫∞011+xadx, where a>1 and a∈R
Any help will be much appreciated.
Answer
Use the change of variables 1+xα=1t to cast the integral in terms of the beta function
1α∫10t−1/α(1−t)1/α−1=1αΓ(1α)Γ(1−1α)
I am trying to evaluate the following:
∫∞011+xadx, where a>1 and a∈R
Any help will be much appreciated.
Answer
Use the change of variables 1+xα=1t to cast the integral in terms of the beta function
1α∫10t−1/α(1−t)1/α−1=1αΓ(1α)Γ(1−1α)
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