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Need advice

  1. Nov 21, 2008 #1
    2. Relevant equations
    Need to integrate x^2/((x^2-1)^(1/2)).

    3. The attempt at a solution
    I first broke the equation into (x^2-1)^(1/2) + (x^2-1)^(-1/2)

    Hence Integral (x^2/((x^2-1)^(1/2))) = Integral((x^2-1)^(1/2)) + Integral((x^2-1)^(-1/2)))

    Further on Integral((x^2-1)^(1/2)) is an integral by parts.

    Hence Integral((x^2-1)^(1/2)) = x(x^2-1)^(1/2) - Integral(x^2/((x^2-1)^(1/2)))

    Therefore Integral (x^2/((x^2-1)^(1/2))) = 1/2(x(x^2-1)^(1/2) + Integral((x^2-1)^(-1/2))

    But now I am stuck on how to solve the Integral((x^2-1)^(-1/2)).

    I am sorry that I can't put this into Latex form as my name suggest I don't know how to use Latex.
  2. jcsd
  3. Nov 21, 2008 #2


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    Science Advisor
    Homework Helper

    I think it's time to try a trig substitution. How about x=sec(u)?
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