What is the integral of ln(x-5) ?

The integral of ln(x-5) is xln(x-5)-5ln(x-5)-x+5+C

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integral of ln(x-5)

\int ln (x - 5) d x

x ln (x - 5) - 5 ln (x - 5) - x + 5 + C

Solution steps

\int ln (x - 5) 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 - 5

= (x - 5) ln (x - 5) - (x - 5)

Simplify

(x - 5) ln (x - 5) - (x - 5) : x ln (x - 5) - 5 ln (x - 5) - x + 5

= x ln (x - 5) - 5 ln (x - 5) - x + 5

Add a constant to the solution

= x ln (x - 5) - 5 ln (x - 5) - x + 5 + C

\frac{d}{d x} ((sin (x))^{3})

x \to 0 lim (\frac{x ^{2}}{x})

f (x) = x^{2} + 9

\frac{d}{d x} (x^{2} sin (π x))

\frac{d y}{d x} = y sec^{2} (x)

What is the integral of ln(x-5) ?
The integral of ln(x-5) is xln(x-5)-5ln(x-5)-x+5+C