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: Integral of sqrt(1 + x^4+ 2x^2)

  1. Aug 18, 2010 #1
    1. The problem statement, all variables and given/known data
    sqrt(1 + x^4+ 2x^2)

    2. Relevant equations

    3. The attempt at a solution
    k so i need a lead on this one, maybe some kind of substition, i am not quite adept with finding the integrals of a square root function with polynomials in it
  2. jcsd
  3. Aug 18, 2010 #2


    User Avatar

    Here's a bit of a hint. When you expand (x+1)^2, what do you get?
  4. Aug 18, 2010 #3


    User Avatar
    Homework Helper

    This problem is rigged to simplify VERY nicely :smile:

    Let x2=u and you should see it more easily.
  5. Aug 18, 2010 #4
    x^2 + 2x + 1
  6. Aug 18, 2010 #5
    ohhh hmm
  7. Aug 18, 2010 #6
    ok i see it now, but if x^2 = u then dx x= du and then dx = du/x does that makes sense ?
  8. Aug 18, 2010 #7
    You can't put du/x inside the integral, the point of the substitution is to get rid of the x's....look at x^4+2x^2+1...there is a way to simplify it similar to how you would simplify x^2+2x+1...you won't need a substitution and then the answer is easy.
  9. Aug 18, 2010 #8
    sorry i am dumb i got it
  10. Aug 18, 2010 #9


    User Avatar
    Homework Helper

    Oh yes sorry I never meant for you to make a substitution in the classic sense of solving an integral, but to make the substitution since u2+2u+1 is easily distinguishable as (u+1)2
  11. Aug 18, 2010 #10


    User Avatar
    Homework Helper

    (1 + x4 + 2x2)1/2

    = [(1 + x2)2]1/2

    = (1 + x2 )

    Now find the integration of (1 + x2)dx
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook