# Thread: Definite integral using contour integration.

1. ## Definite integral using contour integration.

Hi

i need help in solving this integral for this specific integration limit:

int (0) to (pi/2) {cos (2 theta)/(cos(theta)-x)}dtheta abs (x)<1

mopen

2. ## Re: i need help solving this integral.

If the problem has been proposed in the context of complex variable, use the substitution $z=e^{i\theta}$ .

3. ## Re: i need help solving this integral.

yes, i did that but the problem is that i got imaginary part of the solution, but i think the integral should be real.

4. ## Re: i need help solving this integral.

Originally Posted by mopen
yes, i did that but the problem is that i got imaginary part of the solution, but i think the integral should be real.
Indeed, the solution must be real. Please, show your work an we can check it.

5. ## Re: Definite integral using contour integration.

Hi
i have attached two different solution for the problem. from the first one i got unexpected results at low x and at the second one i got imaginary part of the solution.

So any help with the problem!

thanks

mopen