Expert: Paul Klarreich - 3/4/2008

Question
Hi,

I need help with this integration problem:

Directions: Evaluate the indefinite integral.
1. I have uploaded the problem onto here:
http://i25.tinypic.com/2dv1od4.png

I tried splitting it into two different parts but then I got stuck. any ideas?

thank you very much!

Answer
Questioner:   Caroline
Category:  Calculus
Private:  No
 
Subject:  Integration by Substitution
Question:  Hi,

I need help with this integration problem:

Directions: Evaluate the indefinite integral.
1. I have uploaded the problem onto here:
http://i25.tinypic.com/2dv1od4.png

I tried splitting it into two different parts but then I got stuck. any ideas?

thank you very much!
-------------------------------
Hi, Caroline,

Your integral:

{  sin x dx
| ---------
} cos^2(x)

is a standard substitution:

Let u =  cos x,  du = - sin x dx

YOur integral becomes:
{  - du
| ------
}   u^2

{
|  - u^(-2) du
}
- u^(-1)    1      1
-------- = --- = ------
 -1        u    cos x