What is the integral of (x-2)/(x^2-4x-4) ?

The integral of (x-2)/(x^2-4x-4) is 1/2 ln|x^2-4x-4|+C

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integral of (x-2)/(x^2-4x-4)

\int \frac{x - 2}{x ^{2} - 4 x - 4} d x

\frac{1}{2} ln x^{2} - 4 x - 4 + C

Solution steps

\int \frac{x - 2}{x ^{2} - 4 x - 4} d x

Apply u-substitution

: \int \frac{1}{2 u} d u

= \int \frac{1}{2 u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} ln ∣ u ∣

Substitute back

u = x^{2} - 4 x - 4

= \frac{1}{2} ln x^{2} - 4 x - 4

Add a constant to the solution

= \frac{1}{2} ln x^{2} - 4 x - 4 + C

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What is the integral of (x-2)/(x^2-4x-4) ?
The integral of (x-2)/(x^2-4x-4) is 1/2 ln|x^2-4x-4|+C