# How do you use partial fraction decomposition to decompose the fraction to integrate (x+4)/[(x+1)^2 + 4]?

$\frac{x + 4}{{\left(x + 1\right)}^{2} + 4} = \frac{x + 1}{{\left(x + 1\right)}^{2} + 4} + \frac{3}{{\left(x + 1\right)}^{2} + 4}$
we can make one fraction $\frac{w}{{w}^{2} + 4}$ and integrate by substitution to get an $\ln$
and the other integral involves $\frac{3}{{\left(x + 1\right)}^{2} + 4}$ which involves $\arctan$