What is the integral of ln(x-20) ?

The integral of ln(x-20) is xln(x-20)-20ln(x-20)-x+20+C

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integral of ln(x-20)

\int ln (x - 20) d x

x ln (x - 20) - 20 ln (x - 20) - x + 20 + C

Solution steps

\int ln (x - 20) 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 - 20

= (x - 20) ln (x - 20) - (x - 20)

Simplify

(x - 20) ln (x - 20) - (x - 20) : x ln (x - 20) - 20 ln (x - 20) - x + 20

= x ln (x - 20) - 20 ln (x - 20) - x + 20

Add a constant to the solution

= x ln (x - 20) - 20 ln (x - 20) - x + 20 + C

1 + t

x \to 0 + lim (x^{2 \cdot x})

\int_{1}^{\infty} \frac{1}{x + x x} d x

ln (\frac{e ^{x} + 1}{e ^{x} - 1})

\int_{1}^{2} \frac{1}{( 3 - 5 x ) ^{2}} d x

What is the integral of ln(x-20) ?
The integral of ln(x-20) is xln(x-20)-20ln(x-20)-x+20+C