Integrating by Parts: Solving ∫r^3/(4+r^2)^(1/2) dr

[AnnieF]

Homework Statement

∫r^3/(4+r^2)^(1/2) dr

Homework Equations

∫udv=uv-∫vdu

The Attempt at a Solution

I know that integration by parts must be used. I tried doing it with 4+r^2 as u, but kept running into issues..then I got an answer but it appears to be wrong. I guess I am not sure how to do this.

 

[ehild]

First substitute r^2=t, then integrate by parts.ehild

 

[Dick]

I don't think it needs integration by parts. I'd do a simple u substitution. u=r^2+4, like AnnieF suggested. What 'issues' were you running into?

 

[lineintegral1]

I don't think it needs integration by parts. I'd do a simple u substitution. u=r^2+4, like AnnieF suggested. What 'issues' were you running into?

The substitution $u=r^2$ would be significantly easier to deal with. One can then use parts or another substitution to make the integral elementary.