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Integral Rational w/ radical

  1. Mar 15, 2013 #1
    1. The problem statement, all variables and given/known data
    evaluate the integral.


    2. Relevant equations
    [itex]\displaystyle\int {\frac{3x+2}{\sqrt{1-x^2}} dx}[/itex]


    3. The attempt at a solution
    - i tried factoring hoping for a perfect square that i could take the square root of, but that doesn't work.

    -u-sub won't work: u=1-[itex]x^2[/itex] ; du=2x

    -i don't know how to use that denominator in partial fractions.
     
  2. jcsd
  3. Mar 15, 2013 #2

    Curious3141

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    Homework Helper

    Break it up into two:##\int\frac{3x}{\sqrt{1-x^2}}dx + \int\frac{2}{\sqrt{1-x^2}}dx##.

    Observe that ##3x = -\frac{3}{2}*(-2x)##, and now you should be able to make an obvious sub to resolve the first integral.

    For the second integral, just make a simple trig sub.

    Partial fractions wouldn't work here because of that square root in the denominator.
     
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