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A double integral

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Post Thu Jun 01, 2017 7:47 pm

Posts: 48

Prove that

$$\int_{0}^{\infty}xe^{-x}\left(\int_{0}^{\frac{\pi}{2}}(1-e^{x-x\csc{t}})\sec^2{t}dt\right)^2dx=\dfrac{1}{3}$$

I don't have a solution.

Post Fri Jun 02, 2017 9:32 am
Shobhit Site Admin
Site Admin

Posts: 852
Location: Jaipur, India

I have seen this before in the book 'The Cauchy Method of Residues'.


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