I'm trying to solve the following integral:

{ stands for integral

{x^3/(sqrt[x^2 +4]) dx

This is what I have so far:

@ stands for pheta

x=2tan@

dx=2sec^2@ d@

x^2+4=4(1+tan^2@)

Sqrt[x^2+4]=2sec@

Plugging it back in:

{8tan^3@2sec^2@/2sec@ d@

which simplifies to

8{tan^3@sec@ d@

I can't seem to solve this. I've tried integration by parts as well as simple sub.

Where am I going wrong?

Thank you!!