$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}} )$$

Question

$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}} )$$

Prove that
$$\int_{-\infty}^{\infty}\frac{\cos ax}{x^4+1}dx=\frac{\pi}{2}e^{-\frac{a}{\sqrt{2}}}(\cos \frac{a}{\sqrt{2}}+\sin \frac{a}{\sqrt{2}} ).$$

We shouild use the residue theory in Compex analysis.

Complex Analysis Calculus Multivariable Calculus

Kp Yao

18

Report

Answer

The answer is accepted.

Join Matchmaticians Affiliate Marketing Program to earn up to 50% commission on every question your affiliated users ask or answer.

Answer 1

Answers can be viewed only if

The questioner was satisfied and accepted the answer, or
The answer was disputed, but the judge evaluated it as 100% correct.

View the answer

1 Attachment

Erdos

4.6K

$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}} )$$

Answer

Related Questions

Search