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Math Help - Integration: Fraction With 'x' Variable

  1. #1
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    Integration: Fraction With 'x' Variable

    \int \frac{x}{(x^2-1)^\frac12} \ \mathrm{d}x

    There is something really simple that I am not seeing? Help please, Thanks in advance.
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  2. #2
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    Quote Originally Posted by Air View Post
    \int \frac{x}{(x^2-1)^\frac12} \ \mathrm{d}x

    There is something really simple that I am not seeing? Help please, Thanks in advance.
    With the substitution u =x^2 - 1,

    \int \frac{x}{(x^2-1)^\frac12} \ \mathrm{d}x = \frac12 \int \frac{1}{u^\frac12} \ \mathrm{d}u = \frac12 \int u^{-\frac12} \ \mathrm{d}u
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  3. #3
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    Quote Originally Posted by Air View Post
    \int \frac{x}{(x^2-1)^\frac12} \ \mathrm{d}x

    There is something really simple that I am not seeing? Help please, Thanks in advance.
    Substitution, let u = x^2 -1

    Then du = 2x dx

    Your new integral is \int 0.5u^{\frac{-1}{2}} du
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  4. #4
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    Or make z^2=x^2-1.
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