Exercise 19.  Let    be analytic for all z and let C be any contour joining the points  .  
Show that  

        .  

Solution 19.

See text and/or instructor's solution manual.

Solution.  The anti-derivative of     is  .  Thus

                    .

And since    we have

                   .

Equating the integrals we have

                    

And it follows that  

        .  

We are done.   

Aside.  We can let Mathematica double check our work.

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell