1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

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

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted