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IntegralFind the indefinite integral of y=1/(x^2+4x+4)
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We'll write the denominator as the result of expanding the square: x^2 + 4x + 4 = (x+2)^2
We'll re-write the integral:
Int f(x)dx = Int dx/(x+2)^2
We'll use the techinque of changing the variable.
For this reason we'll substitute x+2 by t.
x+2 = t
We'll differentiate both sides:
(x+2)'dx = dt
So, dx = dt
We'll re-write the integral in the variable t:
Int dx/(x+2)^2 = Int dt/t^2
Int dt/t^2 = Int [t^(-2)]*dt
Int [t^(-2)]*dt = t^(-2+1)/(-2+1) + C = t^(-1)/-1 + C = -1/t + C
But t = x+2
Int dx/(x+2)^2 = -1/(x+2) + C
Posted by giorgiana1976 on May 19, 2011 at 11:23 AM (Answer #2)
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