Prove that $\int _0^{\infty} \frac{1}{1+x^{2n}}dx=\frac{\pi}{2n}\csc (\frac{\pi}{2n})$
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.
1 Attachment

4.8K
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 860 views
- $40.00
Related Questions
- Find $\lim\limits _{n\rightarrow \infty} n^2 \prod\limits_{k=1}^{n} (\frac{1}{k^2}+\frac{1}{n^2})^{\frac{1}{n}}$
- Calculus Question
- Two calculus questions
- Existence of golobal minimum point for continuous functions on $\mathbb{R}^2$
- Prove that $\int_{-\infty}^{\infty}\frac{\cos ax}{x^4+1}dx=\frac{\pi}{2}e^{-\frac{a}{\sqrt{2}}}(\cos \frac{a}{\sqrt{2}}+\sin \frac{a}{\sqrt{2}} )$
- Find the extrema of $f(x,y)=x$ subject to the constraint $x^2+2y^2=2$
- Convex subset
-
Find a general solution for the lengths of the sides of the rectangular parallelepiped with the
largest volume that can be inscribed in the following ellipsoid