Problem: Evaluate $\displaystyle \int_0^\infty \left(\dfrac{\sin x}{x} \right)^m dx$.
Approach: So I want to use contour integration to find the desired value. I choose to integrate
$$\displaystyle \int_C \left(\dfrac{e^{iz}}{z} \right)^m dz$$
where $C$ is the semi-circle centered at the origin with radius $R$. However, It does not work because I only give me $\sin(mx)$, not $\sin^m(x)$. How can I do this with complex number approach?
