By expanding the rational function

$\frac{y}{(y+1)(y-5)(y+4)}$

as a sum of three partial fractions, each with linear denominators, or otherwise, find the indefinite integral

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{y}{(y+1)(y-5)(y+4)}dy$

As a sum of partial fractions

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{y}{(y+1)(y-5)(y+4)}dy=1,{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dy}{y+1}+1{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dy}{y-5}+{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dy}{y+4}$

$($Type an integer or a simplified fraction.$)$

Integrating term by term

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{y}{(y+1)(y-5)(y+4)}dy=$

$$

plus a constant of integration.

$($Do not specify another constant of integration in your answer.$)$