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Math Help - How to integrate arccos?

  1. #1
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    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.
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  2. #2
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    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
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