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I can not figure out how to integrate $$\int\frac{3x^2+x+4}{x^3+x} \, dx.$$ I got as far as factoring the denominator which gives us $x(x^2+1)$.

So from there I got $$\frac{3x^2+x+4}{x(x^2+1)} = \frac{A}{x} + \frac{Bx+C}{x^2+1}$$ which would give us: $(3x^2 + x + 4) = A(x^2 + 1) + (Bx+C)x$

This is where Im stuck because I can not figure out the values for $B$ and $C$. Please help.

  • 2
    What have you tried to do in order to find $A$, $B$ and $C$? The procedure to compute the partial fraction decomposition is quite the same every time...2011-03-10
  • 0
    (Also, in the second equation the integral sign should not appear)2011-03-10
  • 2
    See the [Heaviside cover-up method](http://en.wikipedia.org/wiki/Heaviside_cover-up_method) and see this [prior question](http://math.stackexchange.com/questions/23484/help-solving-int-frac8x415x316x222x4xx12x22dx/23498#23498)2011-03-10

3 Answers 3