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: Bonus Integral

  1. Nov 24, 2009 #1
    1. The problem statement, all variables and given/known data
    [tex]\int\frac{\sqrt{1+x}+\sqrt{1-x}} { \sqrt{1+x}-\sqrt{1-x}}{dx}[/tex]

    2. Relevant equations
    I believe trig substitution can be used here. I'm not very good at calculus only beginning to take calc classes, and guideance would be wonderful. because i want to get better.

    3. The attempt at a solution
    I dont have any idea on what to substitute.
    x = some thing like x^2 ??
    or u = 1 - x
    and u = 1 + x ??
  2. jcsd
  3. Nov 24, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    The first thing you want to do is simplify the expression algebraically. It will help to rationalize the denominator by multiplying numerator and denominator by sqrt(1-x)+sqrt(1+x). The trick here is that (sqrt(a)-sqrt(b))*(sqrt(a)+sqrt(b))=a-b. Try simplifying it and see how far you can get.
  4. Nov 24, 2009 #3
    ohhhh, thank you, i cant attempt it at this moment but your solution looks promising !
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook