# 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 $$a+b$$?

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