Reduction formula/Integration by parts problem

[Coffeepower]

Homework Statement

The problem asks me to: Determine a reduction formula for the stated integral (See Picture and problem at:

http://garciarussellchem.angelfire.com/Photo/

Please help me out with this problem. I don't understand why they do not include an extra r in the denominator when integrating dv. I also don't understand what purpose the r^(n-1) serves.

This is a bit confusing.

Thank you.

 

[learningphysics]

They are using $$u = r^{n-1}$$ and $$dv = re^{-ar^2}dr$$ then doing integration by parts with those...

 

[Coffeepower]

This means that v must equal"

v= (re^-(ar^2))/-2ar in order for us to get the dv back right?

THANK YOU FOR THE QUICK REPLY :) !

 

[learningphysics]

No prob.

If you differentiate $$\frac{-1}{2a}e^{-ar^2}$$ you get $$re^{-ar^2}$$, so that's why $$v = \frac{-1}{2a}e^{-ar^2}$$

 

[Coffeepower]

Thanks a bunch.
This site rocks.

(thank you)^(10)