Find the indefinite integral of y=1/(x^2+4x+4)?

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We have to find the integral of y=1/(x^2+4x+4).

Now we see that y = 1 / (x^2+4x+4)

=> y = 1 / (x+2)^2

Let us use the notation p = x+2

We see that dp = dx

=> Int [y/dy ]= Int [dx/ (x+2)^2]

=> Int [ dp / p^2]

Now the integral of x^n = x^(n+1)/ (n+1)

=> Int [ dp / p^2]

=> p^-1/-1

=> -1/p

But p = x+2

Therefore the required integral is -1/(x+2).

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