# How to integrate arccos?

• Feb 28th 2011, 07:41 AM
Kuma
How to integrate arccos?
Hi.

I'm having lots of trouble with the integration of arccos if someone can help. Here is the question.

integral (arccos(root x))^2 dx. or equivalently:
integral (arccos(x^1/2))^2

I'm not sure where to start. Or what substitution I should make.
• Feb 28th 2011, 08:38 AM
e^(i*pi)
$u = \arccos(\sqrt{x}) \implies x = \cos^2 u$

$dx = -2\sin u \cos u du$

$\displaystyle \int \arccos(\sqrt{x})\, dx = \int u \cdot -\sin(2u) du$

Use integration by parts