The hint is to use integration by parts, but I really don't see how to integrate by parts here.
$$\int_{-\infty}^{\infty}\frac{\sin^3 x}{x^3}dx$$
This is a question from a complex analysis class, so I thought I would use something like semicircular contour.
Any help will be appreciated. Thanks!
Hint:
Note that $\sin^3x=\frac{1}{4}(3\sin x-\sin 3x)$. So we only have to find $\int \frac{\sin x} {x^3}dx$. This can be done by using integration by parts repeatedly, first convert it to an integral with integrand $\frac{\cos x} {x^2} $