Example 8.18.  Evaluate  .  

Explore Solution 8.18.

Enter the functions    and    and locate the singularities of  f[z].

Which poles lie in the upper half plane?

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

Remark.  The integral of  F[x] for this problem is  g[x],  but it cannot be used in any meaningful way to solve the problem at hand.

This looks good, however it cannot be used to solve for the definite integral. This does not agree with the answer obtained with the residue calculus.

However, the definite integral will produce the following result.

Which is also the correct answer.

The PrincipalValue option can also be used.

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