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Math Help - another tough integral question..

  1. #1
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    another tough integral question..

    integral of arcsin(x)/x^2

    I know integration by parts must be used but for some reason I can never get it to reduce enough
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  2. #2
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    Quote Originally Posted by khood View Post
    integral of arcsin(x)/x^2

    I know integration by parts must be used but for some reason I can never get it to reduce enough
     v' = \frac{1}{x^2}
     v = -\frac{1}{x}

     u = \arcsin(x)
     u' = \frac{1}{\sqrt{1-x^2}}

     \int v'u = vu - \int u'v

     = \frac{-arcsin(x)}{x} - \int \frac{-1}{x \sqrt{1-x^2}}dx

     = \frac{-arcsin(x)}{x} + \int \frac{1}{x \sqrt{1-x^2}}dx
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