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.

Board index **‹** Computation of Integrals **‹** A double integral
## A double integral

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.

**Moderators:** galactus, Random Variable, sos440

2 posts
• Page **1** of **1**

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

I don't have a solution.

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

2 posts
• Page **1** of **1**