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

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

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integral of ln(4-2x)

\int ln (4 - 2 x) d x

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

Solution steps

\int ln (4 - 2 x) d x

Apply Integration By Parts

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

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

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

Simplify

= x ln (4 - 2 x) - 2 ln ∣ 2 - x ∣ - x

Add a constant to the solution

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

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