Find the integral of g(x) = (x-2)/(x^2-4)

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to find the integral of g(x) = (x-2)/(x^2-4).

g(x) = (x-2)/(x^2-4)

=> g(x) = (x-2)/(x - 2)(x + 2)

=> g(x) = 1/ (x + 2)

Int[g(x)] = Int[ 1/ (x+ 2)]

=> ln (x + 2) + C

The required integral is ln (x + 2) + C

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given that g(x) = (x-2)/(x^2-4)

We need to find the integral of g(x).

First we will simplify.

g(x) = (x-2)/(x-2)(x+2) = 1/(x+2)

==> g(x) = (x+2)^-1

Now we will integrate.

==> Intg g(x) dx = Int (x+2)^-1 dx

We will assume that u= x+2 ==> du = dx

==> Int g(x) dx = Int 1/u du = ln u + c

Now we will substitute back u= x+2

==> Int g(x) = ln (x+2) + C

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