[SOLVED] Simple Antiderivative

[Icebreaker]

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 . :wink:

Daniel.

[Icebreaker]

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...

[Icebreaker]

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 :smile:

Alex