Question

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

Answer 1

`(x+4)/((x+1)^2 + 4) = (x+1)/((x+1)^2+4) + 3/((x+1)^2+4)`

Explanation:

It is not really a partial fraction decomposition, but
we can make one fraction `w/(w^2+4)` and integrate by substitution to get an `ln`

and the other integral involves `3/((x+1)^2+4)` which involves `arctan`