Evaluate the indefinite integral of the fraction 1/(16x^2+24x+9)?

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We have to find the integral of 1/(16x^2+24x+9)

1/(16x^2+24x+9)

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

let 4x + 3 = u

=> du/dx = 4

=> dx = du/4

Int[ 1/(16x^2+24x+9) dx]

=> Int [ 1/u^2 du/4]

=> (1/4) Int [ u^-2 du]

=> (1/4) u^-1/-1

=> (-1/4u) + C

replace u = 4x + 3

=> -1/(16x + 12) + C

The required integral is -1/(16x + 12) + C

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