Results 1 to 5 of 5

Math Help - integration problem

  1. #1
    Newbie
    Joined
    May 2009
    Posts
    6

    integration problem

    hi there,

    can anyone help me understand how to work with this problem?


    ingration of ( x - 2 ) / sqrt (x - 1)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    Let u = sqrt(x-1)

    then du = 1/(2sqrt(x-1) dx

    also u^2 = x-1

    so x-2 = u^2 -1
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member Spec's Avatar
    Joined
    Aug 2007
    Posts
    318
    \frac{x-2}{\sqrt{x-1}}=\frac{x-1}{\sqrt{x-1}}-\frac{1}{\sqrt{x-1}}=\sqrt{x-1}-\frac{1}{\sqrt{x-1}}

    The last expression is easy to integrate.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    May 2009
    Posts
    6
    thanks spec, that was awesome
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,803
    Thanks
    693
    Hello, weskerq8!

    Another approach . . .


    \int \frac{x - 2}{\sqrt{x - 1}}\,dx

    Let: u \:=\:\sqrt{x-1} \quad\Rightarrow\quad u^2 \:=\:x-1 \quad\Rightarrow\quad x \:=\:u^2+1\quad\Rightarrow\quad dx \:=\:2u\,du


    Substitute: . \int\frac{u^2-1}{u}(2u\,du) \;=\;2\int(u^2-1)\,du \;=\;2\left(\frac{u^3}{3} - u\right) + C \;=\;\tfrac{2}{3}u(u^2-3) + C


    Back-substitute: . \tfrac{2}{3}\sqrt{x-1}\bigg[(\sqrt{x-1})^2 - 3\bigg] + C \;=\;\tfrac{2}{3}\sqrt{x-1}\,(x - 1 - 3)

    . . . . . . . . . . . . = \;\tfrac{2}{3}(x-4)\sqrt{x-1} + C

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Integration problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 4th 2010, 09:35 PM
  2. Integration Problem
    Posted in the Calculus Forum
    Replies: 6
    Last Post: March 16th 2010, 04:20 PM
  3. Replies: 2
    Last Post: February 19th 2010, 10:55 AM
  4. Integration problem?
    Posted in the Calculus Forum
    Replies: 6
    Last Post: June 3rd 2009, 06:33 PM
  5. Integration problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 2nd 2008, 02:19 AM

Search Tags


/mathhelpforum @mathhelpforum