What is the integral of ln(x-9) ?

The integral of ln(x-9) is xln(x-9)-9ln(x-9)-x+9+C

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integral of ln(x-9)

\int ln (x - 9) d x

x ln (x - 9) - 9 ln (x - 9) - x + 9 + C

Solution steps

\int ln (x - 9) d x

Apply u-substitution

= \int ln (u) d u

Apply Integration By Parts

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

\int 1 d u = u

= u ln (u) - u

Substitute back

u = x - 9

= (x - 9) ln (x - 9) - (x - 9)

Simplify

(x - 9) ln (x - 9) - (x - 9) : x ln (x - 9) - 9 ln (x - 9) - x + 9

= x ln (x - 9) - 9 ln (x - 9) - x + 9

Add a constant to the solution

= x ln (x - 9) - 9 ln (x - 9) - x + 9 + C

What is the integral of ln(x-9) ?
The integral of ln(x-9) is xln(x-9)-9ln(x-9)-x+9+C