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Homework Help: Splitting Fractions (Integrals)

  1. Apr 10, 2015 #1
    1. The problem statement, all variables and given/known data

    Integrate (2-3x/(Sqrt.(1 - x^2))) dx

    2. Relevant equations
    1/Sqrt.(1-x^2) = arctan

    3. The attempt at a solution
    I am so lost, but this is what I've tried, but didn't work...

    I separated the integral into two so
    Integral of (2/(Sqrt.(1-x^20))) dx - integral of (3x/(Sqrt.(1-x^2))) dx
    I am not sure how to proceed? Help!
  2. jcsd
  3. Apr 10, 2015 #2
    this can be solved using a trig substitution for x. Can you think of what this substitution should be to simplify the denominator?
  4. Apr 10, 2015 #3


    Staff: Mentor

    Looks like a natural for trig substitutions for both integrals
  5. Apr 10, 2015 #4


    User Avatar
    Science Advisor

    I would NOT use a trig substitution for [itex]\frac{3x}{\sqrt{1- x^2}}[/itex]. Instead let [itex]u= 1- x^2[/itex]
  6. Apr 10, 2015 #5


    Staff: Mentor

    A trig substitution would work, but I agree that an ordinary substitution (as you suggest) would be easier, which makes it a better choice.
  7. Apr 10, 2015 #6
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