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Homework Help: Integration of irrational function

  1. Mar 29, 2016 #1
    1. The problem statement, all variables and given/known data
    Find the integral [itex]\int \frac{1}{(x-2)^3\sqrt{3x^2-8x+5}}\mathrm dx[/itex]

    2. The attempt at a solution
    I can't find a useful substitution to solve this integral.
    I tried [tex]x-2=\frac{1}{u},x=\frac{1}{u}+2,dx=-\frac{1}{u^2}du[/tex] that gives
    [tex]\int \frac{1}{(x-2)^3\sqrt{3x^2-8x+5}}\mathrm dx=-\int \frac{u}{\sqrt{3\left(\frac{1}{u}+2\right)^2-8\left(\frac{1}{u}+2\right)+5}}\mathrm du[/tex]

    Is there a useful substitution for [itex]u[/itex]?
  2. jcsd
  3. Mar 29, 2016 #2


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    Factor ##\ 3x^2-8x+5\ ##. Then putting your u substitution into that simplifies things a bit.
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