Hi,

Problem with complex integral.Consider the integral:

$\displaystyle \int_{0}^{\infty}\frac{(x^a-1)}{x^3-1}\,dx$

with the branch -pi/0<phi<3pi/2 and the idented contour at z=0 and z=1

(circular contour in the upper half plane)

a)show that this integral can be written in terms of the integral:

$\displaystyle \pi\frac{(e^{2ia\pi/3}-1)}{(e^{2i\pi/3}-1)sin2\pi/3}$

$\displaystyle +\int_{0}^{\infty}\frac{(x^ae^{ia\pi}-1)}{x^3+1}$

no problem with this.I have found it.

b)Evaluate the second integral in part a)and fiond the value of the original

integral.

$\displaystyle \frac{\pi sin(a\pi/3)}{3sin\pi/3)sin¨[\pi/3(a+1)]}$

with this last integral I hav a problem.I used the contour z=x(0<x<R) the sectorcircle z=Re^i.phi(0<phi<2pi/3)and the line z=xe^2pî/3(0<x<R).

I can't find the result.

The choosen contour????????????

Can somebody give me a suggestion?????????Thanks