Example 6.25.  Show that,  where C is the circle    with positive orientation.

Explore Solution 6.25.

Enter the integrand    and locate the singularities.

Find the singularity that lie inside  .  

Since  z = i  is a singularity of order  n = 4 , multiply the integrand by to obtain the function f(z).

Use Cauchy's Integral Formula for Derivatives to evaluate the integral of   taken over C.

Thus, we have found the value of the contour integral.

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