Example 8.14.  Find the Cauchy principal value of  .

Explore Solution 8.14.

Method (i).  Enter the function    and investigate the  Cauchy Principal Value .

Method (ii).  Enter the function    and locate the singularities.

Determine which poles lie in the upper half plane ?

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

Or, we can use Mathematica's integral table and evaluate the integral.

However, for this simple integral Mathematica's can find the correct answer without resorting to the PrincipalValue option.

The above answer is correct too.

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