## [SOLVED] Simple Antiderivative

How would I compute the antiderivative of

$$\int \sqrt{1-\frac{x^2}{2}}$$

It looks familiar, but I can't quite remember how...

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 Recognitions: Gold Member Homework Help Science Advisor Put $$x=\sqrt{2} \sin u$$ and go from there.
 Blog Entries: 9 Recognitions: Homework Help Science Advisor U can also put the Riemann measure on $\mathbb{R}$ : $dx$. Daniel.

## [SOLVED] Simple Antiderivative

Ah yes, of course. Thanks.

Quick follow-up:

$$\int\log|\sqrt{1-x^2}+x|$$

 Recognitions: Gold Member Homework Help Science Advisor I think that integrand is related to an inverse hyperbolic trig function... but I'd have to play around with it to work out which one. Maybe somebody else...
 Perhaps it simply cannot be expressed algebraically?

 Quote by Icebreaker Perhaps it simply cannot be expressed algebraically?
It cannot be expressed in terms of elementary functions, you are correct.

I love Mathematica

Alex