# [SOLVED] Simple Antiderivative

by Icebreaker
Tags: antiderivative, simple, solved
 P: n/a How would I compute the antiderivative of $$\int \sqrt{1-\frac{x^2}{2}}$$ It looks familiar, but I can't quite remember how...
 PF Patron HW Helper Sci Advisor P: 562 Put $$x=\sqrt{2} \sin u$$ and go from there.
 HW Helper Sci Advisor P: 11,718 U can also put the Riemann measure on $\mathbb{R}$ : $dx$. Daniel.
P: n/a

## [SOLVED] Simple Antiderivative

Ah yes, of course. Thanks.

Quick follow-up:

$$\int\log|\sqrt{1-x^2}+x|$$
 PF Patron HW Helper Sci Advisor P: 562 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...
 P: n/a Perhaps it simply cannot be expressed algebraically?
P: 668
 Quote by Icebreaker Perhaps it simply cannot be expressed algebraically?
It cannot be expressed in terms of elementary functions, you are correct.

I love Mathematica

Alex

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