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Math Help - hard integration

  1. #1
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    hard integration

    S log(x + (x^2 -1)^1/2)dx
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  2. #2
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    Quote Originally Posted by hkdrmark View Post
    S log(x + (x^2 -1)^1/2)dx
    One approach is to use integration by parts:

    \int u\, dv = uv - \int v \, du.

    Let:

    u = \ln (x + \sqrt{x^2 - 1}) \Rightarrow du = \frac{1}{\sqrt{x^2 - 1}}\, (after a modest amount of work),

    dv = dx \Rightarrow v = x.


    For the other five other approaches (where the rest easily follows), await a reply by Krizalid .....
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    that's godly...
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  4. #4
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    Quote Originally Posted by mr fantastic View Post
    For the other five other approaches (where the rest easily follows), await a reply by Krizalid .....
    There's no much here. Integration by parts is the way to tackle integrals like this one.
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