Encouraged by Abhineet Nayyar

Calculus Level 5

\[ \large \int_0^\infty \left( \frac{\sin x}x \right)^5 \, dx \]

If the integral above is equal to \( \dfrac ab \pi \) for coprime positive integers \(a\) and \(b\), find the value of \(a + b + 1 \).