What does e have to do with this integral?

Calculus Level 5

\[\large \displaystyle \int_{-\infty}^{\infty} \dfrac{\cos ^3 {(x)}}{1+x^2} \, dx\]

If the value of the integral above equals to \( \dfrac{\pi^p}q \left( \dfrac r{e^s} + \dfrac t{e^u} \right) \) for positive integers \(p,q,r,s,t\) and \(u\) with \( \gcd (r, q) = \gcd(t, q) = 1 \). Find the value of \(p+q+r+s+t+u\).

×

Problem Loading...

Note Loading...

Set Loading...