# Simple Antiderivative

Icebreaker
[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...

James R
Homework Helper
Gold Member
Put

$$x=\sqrt{2} \sin u$$

and go from there.

dextercioby
Homework Helper
U can also put the Riemann measure on $\mathbb{R}$ : $dx$.

Daniel.

Icebreaker
Ah yes, of course. Thanks.

Quick follow-up:

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

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James R
Homework Helper
Gold Member
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...

Icebreaker
Perhaps it simply cannot be expressed algebraically?

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

I love Mathematica

Alex