Inverse of the sinc function - need to use Ei function?

[thomas49th]

Homework Statement

http://gyazo.com/966f3a03d71843a46a832e6508d6ca95

So when t> 0.5 or t<-0.5 the text says I1 and I2 cancel. Can I show this. When I tried, integration by parts gets me nowhere, so I looked up the integral of form e^x/x and apparently it has "no elementary derivative" - have to use Ei, which I've never heard of. Should I just take it for granted that I1 and I2 cancel?

Also it says about pole being on the real axis, but gives me I1 =i*pi, which is on the imaginary axis. Not quite sure what that part is trying to say

Thanks
Thomas

 

[Dick]

Try applying the change of variables $\omega'=p_1 \omega$ to I1. What do you notice? And no, you don't need the Ei function.