Example 8.22.  Show that  .    

Explore Solution 8.22.

Enter the function and    and locate the singularities.

Which poles lie in the upper half plane ?  Which poles lie on the real axis ?

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

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

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

Which is also the correct answer.

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