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Homework Help: How to calculate an integral

  1. May 14, 2013 #1
    1. The problem statement, all variables and given/known data

    [itex]\int \sqrt {\frac{1+x}{1-x}} dx = [/itex] ?

    The solution is:

    [itex] = \arcsin{x} -\sqrt{1-x^2} + const[/itex]

    If someone could help me to find the solution I'll be very pleased! :-)
    Thanks everybody!
  2. jcsd
  3. May 14, 2013 #2
    Try multiplying the integrand by [itex]\frac{\sqrt{1+x}}{\sqrt{1+x}}[/itex] and remember that [itex](1+x)(1-x) = 1 - x^2[/itex]. If you consider what the derivative of [itex]arcsin(x)[/itex] is, it's easier to see what you should be trying to do to the integral. You may also need to do a substitution.
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