How can the Fourier Transform be used to solve for the integral of (sinx)^n/x^n?

[bodensee9]

Homework Statement

Can someone please help me with this problem. I am wondering how I would be able to calculate the integral of (sinx)^n/x^n using the Fourier Transform? I am given these formulas for the Fourier Transform of spaces of square integrable functions. SO I know that the integral of the product of 2 square integrable functions is equal to the integral of the product of 1 of the functions evaluated at positive xi, and the other function evaluated at negative xi. But besides that, how should I even approach this probleme? Thanks very much!

Homework Equations

The Attempt at a Solution

 

[lippyka]

I think that the best approach to this problem would be to use the Fourier Transform and then use the inverse Fourier Transform to solve for the integral. First, we would need to define our function (sinx)^n/x^n as a Fourier Transform of some square integrable function. Then, we would take the Fourier Transform of this function and evaluate it at both positive and negative xi. Finally, we would use the inverse Fourier Transform to calculate the integral of (sinx)^n/x^n. I hope this helps!