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Homework Help: Integral of x sqrt( x/(x-1))

  1. Aug 18, 2010 #1
    1. The problem statement, all variables and given/known data
    integral of x *sqrt( x/(x-1))

    2. Relevant equations

    3. The attempt at a solution
    I honestly don't know how to approach this i dont see any type of trig substituions whatsover, I really need some kind of lead and an explnation y that method works
  2. jcsd
  3. Aug 18, 2010 #2


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    Hmmm... I guess I'd start by making the substitution [itex]u=\frac{x}{x-1}=1+\frac{1}{x-1}[/itex] in order to get rid of the junk inside the square root. You'll probably find that doing this will allow you to split the integral into two easier integrals since [itex]x=1+\frac{1}{u-1}[/itex]
  4. Aug 18, 2010 #3


    Staff: Mentor

    I haven't carried this all the way through, but I think it will work
    [tex]\int x \sqrt{\frac{x}{x - 1}}dx = \int \frac{x^{3/2}}{\sqrt{x - 1}}dx[/tex]

    I believe that an ordinary substitution will work.
    Let u = sqrt(x - 1).
  5. Aug 18, 2010 #4
  6. Aug 18, 2010 #5


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    You can integrate secn θ using integration by parts, letting u=secn-2 θ and dv=sec2 θ dθ. For sec5 θ, you'll have to do it twice. It's a bit tedious but straightforward.
  7. Aug 18, 2010 #6


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    You don't actually need a trig sub. You can also use Partial Fraction Decomposition if you find that easier.
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