# Integration of a reciprocal function

1. Jun 4, 2012

### Shawn Garsed

1. The problem statement, all variables and given/known data
Evaulate the integral of (4-x2)-3/2.

2. Relevant equations
integration by parts
u-replacement

3. The attempt at a solution
Too long to write it all down, but I used the aforementioned equations. Basically, I'd like somebody to give me a hint about how or where to start, since everything I tried so far hasn't worked.

2. Jun 4, 2012

### EulersFormula

Is this an indefinite integral?

3. Jun 4, 2012

yes, it is

4. Jun 4, 2012

### dextercioby

Do you know the rules of substitution ?

5. Jun 4, 2012

### SammyS

Staff Emeritus
What did you use for the substitution? What did you use for the parts of the integration by parts?

We can give much better help if you show us what you've done. Besides that, it's part of the rules for Homework help in this Forum.

6. Jun 4, 2012

### Shawn Garsed

Yes, that's what I meant by u-replacement. Sorry if that wasn't clear.

7. Jun 4, 2012

### HallsofIvy

Staff Emeritus
Generaly speaking, integrals that involve roots of squares call out for a trig substitution. What happens if you let $x= 2 sin(\theta)$?

8. Jun 4, 2012

### Shawn Garsed

I've used 4-x2, (4-x2)-1/2 and (4-x2)
1/2
as a substitution.

9. Jun 4, 2012

### Shawn Garsed

Thanks HallsofIvy, I got it now. It's x/(4(4-x2)1/2).