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

= \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 - 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

f (x) = 3 x^{4}, at x = - 2

\frac{8 x ^{2}}{4 - 3 x}

x^{2} - 4, - x^{2} + 4

\frac{d}{d x} ((3 x + 8) x^{2})

\int 4 csc (x) cot (x) - sec (x) tan (x) d x

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