Integrating (2-x^2)^{3/2}: Easy or Not?

[Saladsamurai]

Integral of (2-x^2)^{3/2} ?

Homework Statement

I am doing an iterated integral and I am stuck at $$\int(2-x^2)^{3/2}dx$$

Should this be easy or did I mess up in a previous step? I think it should be easy...

EDIT: by "easy" I am mean do I need a table? Or is it something that can be done with a substitution expediently?

 

[jeffreydk]

I don't think you can do that by substitution; I plugged it into mathematica just for the heck of it and it's

$$\int(2-x^2)^{3/2}dx = -\frac{x\sqrt{2-x^2}(x^2-5)}{4}+\frac{3}{2}\tan^{-1}(\frac{x}{\sqrt{2}})$$

so make what you will of that. I'd just try going at it with different by parts or identities.