Integration by parts problem

1. Nov 12, 2006

raincheck

"Evaluate the integral [0,1] x^3/sqrt[x^2 + 1] by integration by parts"

I know I have to use the integration by parts equation, but I don't know what to make u and what to make dv..

2. Nov 12, 2006

Hootenanny

Staff Emeritus
Try rewriting the integral thus;

$$\int^{1}_{0}\; \frac{x^{3}}{\sqrt{x^2+1}} \; dx = \int^{1}_{0}\; x^3 (x^2 +1)^{-\frac{1}{2}} \;dx$$

Now, to determine which term to make u and dv, think about which one will simplify your expression most when you differentiated it and set this to u.

3. Nov 12, 2006

Repetit

You could start by rewriting the integrand:

$$\frac{x^3}{\sqrt{x^2+1}}=x^3 (x^2+1)^{-1/2} = [x^{-6} (x^2+1)]^{-1/2}$$

And the apply the integration by parts formula. That should make it easier.

4. Nov 12, 2006

raincheck

OH okay, thank you!

5. Nov 12, 2006

Max Eilerson

Do you have to do it by parts? Much easier to substitute $$u = x^2$$