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Solve the integral

  1. Apr 17, 2016 #1
    1. The problem statement, all variables and given/known data
    ∫sqrt((x+1)/(x-1))

    2. Relevant equations


    3. The attempt at a solution
    t=sqrt((x+1)/(x-1)), t^2=(x+1)/(x-1)⇒x=(-t^2-1)/(-t^2+1) dx=dt⇒ -4t/((t^2-1)^2)
    ∫t*-4t/((t^2-1)^2)=-4∫t^2+1-1/((t^2+1)^2)=-4∫dt/t^2+1-4∫dt/((t^2-1)^2)
     
  2. jcsd
  3. Apr 17, 2016 #2

    SteamKing

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    Please post calculus HW problems in the Calculus HW forum.
     
  4. Apr 17, 2016 #3

    SammyS

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    Hello Alex235123. Welcome to PF !

    It's really not proper to leave the dx out of the integral. It's especially important when using substitution.

    Consider multiplying the numerator and denominator by x+1, then simplifying the integrand.

    The substitution x = cosh(t) looks like it works well.
     
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