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

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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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