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Math Help - Partial Fraction Decomp Integral

  1. #1
    Member VitaX's Avatar
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    Partial Fraction Decomp Integral

    \int \frac{6x^2 - 10x + 1}{(x-2)(x-1)^2} dx
    Can someone explain the partial fraction decomposition part of this problem. I'll be able to take the integrating from there, just need help in understanding this concept.
    I know you write it as \frac{A}{x-2} + \frac{B}{x-1} + \frac{C}{(x-1)^2}
    If someone could explain how to go about doing the next parts that would be great.
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  2. #2
    Junior Member
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    Quote Originally Posted by VitaX View Post
    \int \frac{6x^2 - 10x + 1}{(x-2)(x-1)^2} dx
    Can someone explain the partial fraction decomposition part of this problem. I'll be able to take the integrating from there, just need help in understanding this concept.
    I know you write it as \frac{A}{x-2} + \frac{B}{x-1} + \frac{C}{(x-1)^2}
    If someone could explain how to go about doing the next parts that would be great.
    Solve for A,B,C for 6x^2 - 10x + 1 = A(x-1)^2+B(x-1)(x-2)+C(x-2)

    Now see what happens when you sub x=1,-2
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