# 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