Solve Indefinite Integral (x^3)sqrt((x^2)+4)dx

[razorlead]

Homework Statement

Indefinite Integral

(x^3)sqrt((x^2)+4)dx

Homework Equations

With an x= 2tan@
and dx= 2 (sec^2)@ d@

The Attempt at a Solution

I get to
8(tan^3)@(sqrt((4tan^2)@+(8sec^2)@d@

Simplified down to

8(tan^3)@(sqrt((12tan^2)@+8d@

After that I'm stuck

The answer is

(1/5)((x^2)+4)^(5/2)-(4/3)((x^2)+4)^(3/2)+C

Thanks very much to the posters on my previous thread

 

[Dick]

Try an algebraic substitution before you jump into trig, like u^2=x^2+4.