Integration of a reciprocal function

[Shawn Garsed]

Homework Statement

Evaulate the integral of (4-x²)^-3/2.

Homework Equations

integration by parts
u-replacement

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.

 

[EulersFormula]

Is this an indefinite integral?

 

[Shawn Garsed]

yes, it is

 

[dextercioby]

Do you know the rules of substitution ?

 

[SammyS]

Homework Statement

Evaulate the integral of (4-x²)^-3/2.

Homework Equations

integration by parts
u-replacement

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.

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.

 

[Shawn Garsed]

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

 

[HallsofIvy]

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

 

[Shawn Garsed]

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

 

[Shawn Garsed]

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