What is the integral of ln(x-3) ?

The integral of ln(x-3) is xln(x-3)-3ln(x-3)-x+3+C

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integral of ln(x-3)

\int ln (x - 3) d x

x ln (x - 3) - 3 ln (x - 3) - x + 3 + C

Solution steps

\int ln (x - 3) 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 - 3

= (x - 3) ln (x - 3) - (x - 3)

Simplify

(x - 3) ln (x - 3) - (x - 3) : x ln (x - 3) - 3 ln (x - 3) - x + 3

= x ln (x - 3) - 3 ln (x - 3) - x + 3

Add a constant to the solution

= x ln (x - 3) - 3 ln (x - 3) - x + 3 + C

f (x) = \frac{2}{x - 5}, at x = 7

\int (x^{2} + 1) (4 x - 3) d x

\int \frac{4 x ^{3}}{1 - x ^{4}} d x

\int x^{5} 6 x^{6} + 2 d x

\int (4 x^{2} + 3)^{2} d x

What is the integral of ln(x-3) ?
The integral of ln(x-3) is xln(x-3)-3ln(x-3)-x+3+C