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

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Answer 1 · 2015-08-31T16:08:36

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

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 $arctan$

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