Help with integration (1) involving integration by parts etc

[NCyellow]

Homework Statement

Solve for indefinite integral of
(7x^3)/sqr(4+x^2)(dx)

Homework Equations

I just can't seem to find the right solution.

The Attempt at a Solution

First of all, we can just factor the 7 out of the integral for now since it is only a constant.
the inverse square root of (4+x^2) looks like arctan(x/2).
So I set 1/(4+x^2) up as dv, and so V would equal arctan(x/2). U is then x^3, and du is 3x^2.
However, the integrals just don't seem to simplify. Please help.

 

[lanedance]

how about looking at trig substitution - in particular what trig identity could simplfy the denominator

 

[Dick]

Substitution again. Try u=x^2+4. You have a left over x^2 in the numerator. But x^2=u-4. Try the easy stuff before you resort to the hard stuff.

 

[NCyellow]

I did it, and ended up with the integral of (u^2-4u) over square root of u, all multiplied by the constant 7/2. After a lengthy algebra session, I ended up with a huge answer, that wasn't correct... What did I do wrong?

 

[Dick]

I ended up with basically (u-4)*du/sqrt(u) forgetting the constants. What did you do? I think you have an extra u in the numerator which doesn't belong there.

 

[NCyellow]

Ah, there we go. I forgot to take out an x for du. Thanks.