Example 8.23.  Evaluate  ,  where  .  

Explore Solution 8.23.

Enter the function and    and locate the isolated singularities.

Which pole(s) are non-zero ?

Compute the residues at  ,  and use the residue calculus to compute the value of the integral.

Aside. We can use Mathematica's built in "PrincipalValue" option to evaluate this definite integral .

Which is also the correct answer.

(c) 2006 John H. Mathews, Russell W. Howell