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Math Help - nonlinear partial fractions

  1. #1
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    nonlinear partial fractions

    \int\frac{x^3+x^2+2x+1}{(x^2+1)(x^2+2)}dx
    so I got (Ax+B)(x^2+2)+(Cx+D)(x^2+1) = x^3+x^2+2x+1
    If I factor an x out of everything but the D constant, and set x=0 then I know D=1 but I'm stuck on how to find the value of the other constants.

    also \int\frac{x^3+4}{x^2+4}dx

    answer 1: .5\ln(x^2+1)+(1+/\sqrt2)\arctan(x/\sqrt2)+C
    answer 2: .5x^2-2\ln(x^2+4)+2\arctan(x/2)+C
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  2. #2
    Senior Member apcalculus's Avatar
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    Quote Originally Posted by superdude View Post
    \int\frac{x^3+x^2+2x+1}{(x^2+1)(x^2+2)}dx
    so I got (Ax+B)(x^2+2)+(Cx+D)(x^2+1) = x^3+x^2+2x+1
    If I factor an x out of everything but the D constant, and set x=0 then I know D=1 but I'm stuck on how to find the value of the other constants.

    also \int\frac{x^3+4}{x^2+4}dx

    answer 1: .5\ln(x^2+1)+(1+/\sqrt2)\arctan(x/\sqrt2)+C
    answer 2: .5x^2-2\ln(x^2+4)+2\arctan(x/2)+C
    A+C = 1
    B+D = 1
    2A+C = 2
    2B+D = 1

    I think these should work:
    A = 1 , C = 0, B = 0, D = 1
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