Using integral calculus integrate the function dy/y^2+8y+20

In other words, we'll have to calculate the indefinite
integral of the given
function:

Int dy/(y^2+8y+20)

We
can re-write the denominator by completing the
square:

(y^2+8y+16) - 16 + 20 = (y+4)^2 + 4 = (y+4)^2 +
2^2

Int dy/(y^2+8y+20) = Int dy/[(y+4)^2 +
2^2]

We'll note y + 4 = t => dy =
dt

Int dy/[(y+4)^2 + 2^2] = Int dt/(t^2 +
2^2)

Int dt/(t^2 + 2^2) = (1/2)*arctan (t/2) +
c

The final result is: Int dy/(y^2+8y+20) =
(1/2)*arctan [(y+4)/2]+ c