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: Finding factors in order to use U sub

  1. Apr 21, 2014 #1
    1. The problem statement, all variables and given/known data

    [tex]\displaystyle{\int}\dfrac{x}{\sqrt{x^2+x+1}}~dx =

    \displaystyle{\int}\dfrac{(x+\frac 1 2)-\frac 1 2}{\sqrt{(x+\frac 1 2)^2+(\frac {\sqrt 3} 2)^2}}~dx[/tex]

    2. Relevant equations


    3. The attempt at a solution

    The solution is given, but I'm not sure how it was found. Is there a method for finding those factors or is it trial and error/intuition?
  2. jcsd
  3. Apr 21, 2014 #2


    Staff: Mentor

    There is a method. They are completing the square in the quadratic in the denominator.
    x2 + x + 1 = x2 + x + (1/4) + (1 - 1/4)
    = (x + 1/2)2 + 3/4
    = (x + 1/2)2 + (√(3)/2)2

    Then they are working with the numerator to get it as you see it in the expression on the right of what you posted.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted