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Math Help - Inverse Trig Integration

  1. #1
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    Inverse Trig Integration

    I am trying to integrate arcsin (x^(1/2)).

    I used a u-sub for x^(1/2) and tried to finish with integration by parts, but I ended up with something just as complicated, requiring another integration by parts. I think I'm going about it the wrong way...
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  2. #2
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    Quote Originally Posted by veronicak5678 View Post
    I am trying to integrate arcsin (x^(1/2)).

    I used a u-sub for x^(1/2) and tried to finish with integration by parts, but I ended up with something just as complicated, requiring another integration by parts. I think I'm going about it the wrong way...
    Showing your work would help. After integration by parts you should get an integral looking like \int \frac{\sqrt{x}}{\sqrt{1-x}} \, dx. Is this integral the cause of your trouble?
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  3. #3
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    After integrating by parts, I end up with

    u^2 sin ^-1 [u] - int ((u^2) / (1-u^2)^(1/2))
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    Quote Originally Posted by veronicak5678 View Post
    After integrating by parts, I end up with

    u^2 sin ^-1 [u] - int ((u^2) / (1-u^2)^(1/2))
    Integration by parts formula: \int u \, dv = uv - \int v \, du.

    I = \int \arcsin (\sqrt{x}) \, dx.

    Make the following choice:

    u = \arcsin (\sqrt{x}) \Rightarrow du = - \frac{1}{2 \sqrt{x} \, \sqrt{1 - x}}.

    dv = dx \Rightarrow v = x.

    Then I = x \, \arcsin (\sqrt{x}) - \frac{1}{2} \int \frac{\sqrt{x}}{\sqrt{1 - x}} \, dx.

    Now refer to post #2.
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