We have to integrate [1/ (y^2 + 8y + 20) dy]
Int [1/( y^2 + 8y + 20) dy]
=> Int [ 1 / (y^2 + 8y + 16 + 4) dy]
=> Int [ 1/((y + 4)^2 + 2^2) dy]
if u = y + 4 , dy = du
=> Int [ 1/ ( u^2 + 2^2) du]
=> (1/2)*arc tan (u /2) + C
substitute u = y + 4
=> (1/2)*arc tan[(y + 4)/2] + C
The required integral is (1/2)*arc tan[(y + 4)/2] + C
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