Simple Antiderivative

[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]

Put

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

and go from there.

 

[dextercioby]

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

Daniel.

 

Ah yes, of course. Thanks.

Quick follow-up:

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

 

[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...

 

Perhaps it simply cannot be expressed algebraically?

 

[amcavoy]

Perhaps it simply cannot be expressed algebraically?

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

I love Mathematica

Alex