Plenty of Integrate by Parts Part 2?
Calculus
Level
5
You are given that \[ \displaystyle \int_0^\infty \frac { \sin x}{x} \, d x = \frac {\pi}{2}. \] If the value of \[\displaystyle \int_0^\infty \frac { \sin^8 x}{x^4} \, dx \] is equal to \( \dfrac ab\pi\) for coprime positive integers \(a\) and \(b\). What is the value of \(a+b\)?
by
Pi Han Goh