∫ (x^2)/ [square root (x^2 +20)] dx

this is another problem assigned in my homework and im just really confused on what to do.. on how to use both.. help appreciated!

- January 17th 2011, 07:22 PMtennis0216Evaluate the integral by using substitution prior to integration by parts
∫ (x^2)/ [square root (x^2 +20)] dx

this is another problem assigned in my homework and im just really confused on what to do.. on how to use both.. help appreciated! - January 17th 2011, 07:24 PMdwsmith
- January 17th 2011, 07:40 PMtennis0216
- January 17th 2011, 07:41 PMdwsmith
- January 17th 2011, 07:54 PMtennis0216
- January 17th 2011, 07:57 PMdwsmith
- January 18th 2011, 07:50 AMHallsofIvy
- January 18th 2011, 08:05 AMProve It
- January 18th 2011, 08:35 AMHallsofIvy
I think you intended . That is, the tangent is not squared.

That way

and

The integral becomes

which, switching to sine and cosine, becomes

Since that has an odd power of cosine, I would suggest multiplying both numerator and denominator by , and then letting so that .

a rational integral that can by done by "partial fractions". - January 18th 2011, 11:44 AMSammyS
- January 18th 2011, 12:47 PMSammyS

Integration by parts:

Therefore, - January 18th 2011, 11:35 PMTheCoffeeMachine
This integral demonstrates the simplicity/efficiency of hyperbolic substitutions! (Cool)

Let , then: