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Math Help - integrate

  1. #1
    Rui
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    integrate

    integrate 1/(x^3 + 2x^2- x-2) dx
    i know have to use partial fractions.
    A/ (x^2-1) + B /(x+2) = 1/ (x^3 + 2x^2- x-2)

    and found B =1/3 and A =1/3 or 1 (don't know which one to use so i used A= 1/3)

    after integrate i got ln(3x^2-3) + ln(3x+6) not sure if it is right..but i have a feeling that it's wrong. Help!
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  2. #2
    Eater of Worlds
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    You didn't finish factoring.

    \frac{A}{x-1}+\frac{B}{x+1}+\frac{C}{x+2}

    Now, it's easier, huh?.

    \lim_{x\rightarrow{1}}\frac{x-1}{(x-1)(x+1)(x+2)}=\frac{1}{6}

    \lim_{x\rightarrow{-1}}\frac{x+1}{(x-1)(x+1)(x+2)}=\frac{-1}{2}

    \lim_{x\rightarrow{-2}}\frac{x+2}{(x-1)(x+1)(x+2)}=\frac{1}{3}

    \frac{1}{6(x-1)}-\frac{1}{2(x+1)}+\frac{1}{3(x+2)}

    Now, integrate.
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  3. #3
    Moo
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    Hello,

    i know have to use partial fractions.
    A/ (x^2-1) + B /(x+2) = 1/ (x^3 + 2x^2- x-2)
    False

    Ok (x^3+2x^2-x-2)=(x^2-1)(x+2), but you have to continue. (x^2-1)=(x-1)(x+1)

    So (x^3+2x^2-x-2)=(x-1)(x+1)(x+2)

    Thus you have to find A, B, C such that :

    \frac{1}{x^3+2x^2-x-2}=\frac{A}{x-1}+\frac{B}{x+1}+\frac{C}{x+2}


    A/ (x^2-1)
    More generally, if you have a term of degree 2 in the denominator, you should have a polynomial of degree 1 in the numerator.

    So here, it should have been \frac{Ax+A'}{x^2-1}

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