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Integral quick q , integrate ((1-x)/(1+x))^1/2

  1. Jan 30, 2017 #1
    1. The problem statement, all variables and given/known data

    How do I go about integrating
    ##(\frac{1-x}{1+x})^{\frac{1}{2}} ##?

    2. Relevant equations
    above

    3. The attempt at a solution
    im not really sure.
    could integrate by partial fractions if it was to the power of ##1##, only thing i can think of

    thanks in advance
     
  2. jcsd
  3. Jan 30, 2017 #2

    RUber

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    Homework Helper

    What if you multiplied by 1,
    i.e.
    ## 1= \frac{\sqrt{1-x}}{\sqrt{1-x}}##
    Then you might have something that looks like a known integral using trig functions.
     
  4. Jan 30, 2017 #3
    oh thanks, so by doing that I get ##\int \frac{1-x}{(1-x^{2})^{1/2}} dx ##, which I can partial fraction and then integrate
     
  5. Jan 30, 2017 #4

    RUber

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    Homework Helper

    I'm not sure if my definition of partial fractions is the same as yours, but
    ##\int \frac{1}{\sqrt{1 -x^2} }\, dx ## and ##\int \frac{x}{\sqrt{1 -x^2}} \, dx## both have known integrals.
     
  6. Jan 30, 2017 #5

    Mark44

    Staff: Mentor

    Partial fractions isn't appropriate here, either. Assuming you could break up ##(\frac{1-x}{1-x^2})^{1/2}## into ##(\frac{A}{1-x} + \frac B {1 + x})^{1/2}##, you still have the sum of the two fractions being raised to the 1/2 power.

    Trig substitution is definitely the way to go after applying @RUber's suggestion.
     
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