What is the integral of ln|x-2| ?

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

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integral of ln|x-2|

\int ln ∣ x - 2 ∣ d x

x ln ∣ x - 2 ∣ - x + 2 - 2 ln ∣ x - 2 ∣ + C

Solution steps

\int ln ∣ x - 2 ∣ d x

Apply Integration By Parts

: x ln ∣ x - 2 ∣ - \int \frac{x}{x - 2} d x

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

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

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

Simplify

= x ln ∣ x - 2 ∣ - x + 2 - 2 ln ∣ x - 2 ∣

Add a constant to the solution

= x ln ∣ x - 2 ∣ - x + 2 - 2 ln ∣ x - 2 ∣ + C

y^{^{'}} = y x, y (1) = 7

\int_{4}^{9} (3 x) d x

y = x^{2} + 2

x \to \infty lim (\frac{x ^{2}}{e ^{x^{3}}})

\frac{d}{d x} (17 cos (x))

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