What is the integral of ln(x-4) ?

The integral of ln(x-4) is xln(x-4)-4ln(x-4)-x+4+C

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integral of ln(x-4)

\int ln (x - 4) d x

x ln (x - 4) - 4 ln (x - 4) - x + 4 + C

Solution steps

\int ln (x - 4) 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 - 4

= (x - 4) ln (x - 4) - (x - 4)

Simplify

(x - 4) ln (x - 4) - (x - 4) : x ln (x - 4) - 4 ln (x - 4) - x + 4

= x ln (x - 4) - 4 ln (x - 4) - x + 4

Add a constant to the solution

= x ln (x - 4) - 4 ln (x - 4) - x + 4 + C

x \to 1 + lim (x^{\frac{1}{x - 1}})

\frac{d y}{d x}, x y = 7

\int \frac{2 x ^{2}}{x ^{2} - 1} d x

\frac{d y}{d x} = e^{4 x} + 9 y

What is the integral of ln(x-4) ?
The integral of ln(x-4) is xln(x-4)-4ln(x-4)-x+4+C