Solving the Antiderivative of sqrt(1-(x^2/2))

[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]

Put

x=\sqrt{2} \sin u

and go from there.

 

[dextercioby]

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|

 

[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

Alex