# Plenty of Integrate by Parts?

Calculus Level 4

Given that $$\large \displaystyle \int_0^\infty \dfrac { \sin x}{x} \, dx = \dfrac {\pi}{2}$$.

If the value of $$\large \displaystyle \int_0^\infty \dfrac { \sin^9 x}{x} \, dx = \dfrac {a\pi}{b}$$ for coprime positive integers $$a$$ and $$b$$, what is the value of $$a+b$$?

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