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

The integral of ln(2x-4) is xln(2x-4)-x+2-2ln|x-2|+C

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integral of ln(2x-4)

\int ln (2 x - 4) d x

x ln (2 x - 4) - x + 2 - 2 ln ∣ x - 2 ∣ + C

Solution steps

\int ln (2 x - 4) d x

Apply Integration By Parts

: x ln (2 x - 4) - \int \frac{x}{x - 2} d x

= x ln (2 x - 4) - \int \frac{x}{x - 2} d x

\int \frac{x}{x - 2} d x = x - 2 + 2 ln ∣ x - 2 ∣

= x ln (2 x - 4) - (x - 2 + 2 ln ∣ x - 2 ∣)

Simplify

= x ln (2 x - 4) - x + 2 - 2 ln ∣ x - 2 ∣

Add a constant to the solution

= x ln (2 x - 4) - x + 2 - 2 ln ∣ x - 2 ∣ + C

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