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

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

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integral of ln(x-2)

\int ln (x - 2) d x

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

Solution steps

\int ln (x - 2) d x

Apply u-substitution

: \int ln (u) d u

= \int ln (u) d u

Apply Integration By Parts

: u ln (u) - \int 1 d u

= u ln (u) - \int 1 d u

\int 1 d u = u

= u ln (u) - u

Substitute back

u = x - 2

= (x - 2) ln (x - 2) - (x - 2)

Simplify

(x - 2) ln (x - 2) - (x - 2) : x ln (x - 2) - 2 ln (x - 2) - x + 2

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

Add a constant to the solution

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

y = \frac{1}{x ^{3}}, (1, 1)

f (x) = \frac{5 x}{x - 3}, (4, 20)

y = (x + 5)^{\frac{1}{x}}

\int x^{2} (x^{3} + 5)^{9} d x

\frac{d}{d x} (\frac{x ^{2} - 1}{x ^{3} - x})

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