Hello, I have been having trouble with trig substitution. I feel that I understand the basic concepts, but I am struggling to get the same answers as the key. I will use @ symbols instead of thetas

Indefinite Integral

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

With an x= 2tan@

and dx= 2 (sec^2)@ d@

I get 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