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Integration using the reduction formula

  1. Feb 12, 2012 #1
    Read the math in the image below


    Is it possible to integrate the rational function using that reduction formula. If yes, how do I go about doing it?

    Keep it simple, I'm new to this (And I missed a lesson)

  2. jcsd
  3. Feb 12, 2012 #2


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    You have
    $$I_n = \int \frac{x^n}{\sqrt{ax+b}}\,dx$$ so you're starting with n=2. When you apply the formula and simplify, you should get
    $$I_2 = \frac{x^2\sqrt{4x+5}}{10} - I_1$$ You made a mistake in the coefficient of I1, so recheck your work getting the second line. Now apply the same formula to expand I1. You'll end up with an expression with I0 which you should know how to integrate.
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