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!

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


    User Avatar
    Homework Helper
    Gold Member

    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


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    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


    User Avatar
    Homework Helper
    Gold Member

    You don't actually need a trig sub. You can also use Partial Fraction Decomposition if you find that easier.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Integral sqrt Date
Integral sqrt((5-x)/x) Dec 31, 2017
Integral sqrt(x)*e^-x Nov 5, 2016
For the life of me I can't solve this integral sqrt(1-x^3) Jul 26, 2016
Integrate x/sqrt(a^2+b^2-2abx) Sep 15, 2014
Integrate sqrt(1+4x^2) Jan 21, 2014