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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

    Dick

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    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 !
     
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