Simple Antiderivative

1. Oct 5, 2005

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...

2. Oct 5, 2005

James R

Put

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

and go from there.

3. Oct 6, 2005

dextercioby

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

Daniel.

4. Oct 6, 2005

Icebreaker

Ah yes, of course. Thanks.

Quick follow-up:

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

Last edited by a moderator: Oct 6, 2005
5. Oct 6, 2005

James R

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...

6. Oct 6, 2005

Icebreaker

Perhaps it simply cannot be expressed algebraically?

7. Oct 6, 2005

amcavoy

It cannot be expressed in terms of elementary functions, you are correct.

I love Mathematica

Alex