Integration - Partial Fraction Decomposition

$\displaystyle \int \frac{x^2 + 3x + 1}{x^4 + 5x^2 + 4}dx$

So first step would be factoring the denominator. $\displaystyle x^4 + 5x^2 + 4 = (x^2 + 1)(x^2 + 4)$

$\displaystyle \int \frac{x^2 + 3x + 1}{(x^2 + 1)(x^2 + 4)}dx$

$\displaystyle \frac{A}{(x^2 + 1)} + \frac{Bx + C}{(x^2 + 4)}$

$\displaystyle x^2 + 3x + 1 = A(x^2 + 4) + (Bx + C)(x^2 + 1)$

Do I have this set up correctly so far?

If so next step would be to find A, so you let x = 0 I believe.

$\displaystyle 0^2 + 3(0) + 1 = A(0^2 + 4) \rightarrow 1 = 4A \rightarrow A = \frac{1}{4}$

To find C, let x = 0 $\displaystyle 0^2 + 3(0) + 1 = 4A + (B(0) + C)(0^2 +1) \rightarrow 1 = 4\left(\frac{1}{4}\right) + C \rightarrow C = 1$

If this is correct so far how would I find B, if this is not correct can someone guide me along here?