What is the integral of ln(x+16) ?

The integral of ln(x+16) is xln(x+16)+16ln(x+16)-x-16+C

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integral of ln(x+16)

\int ln (x + 16) d x

x ln (x + 16) + 16 ln (x + 16) - x - 16 + C

Solution steps

\int ln (x + 16) 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 + 16

= (x + 16) ln (x + 16) - (x + 16)

Simplify

(x + 16) ln (x + 16) - (x + 16) : x ln (x + 16) + 16 ln (x + 16) - x - 16

= x ln (x + 16) + 16 ln (x + 16) - x - 16

Add a constant to the solution

= x ln (x + 16) + 16 ln (x + 16) - x - 16 + C

\frac{d}{d x} (ln (x) \cdot ln (x))

\int_{- 1}^{1} \frac{x}{x ^{2} + x - 6} d x

\int \frac{x ^{2}}{256 - x ^{2}} d x

(tan^{2} (x))^{^{'}}

x \to 5 lim (\frac{( 13 - 4 x ^{2} + 69 )}{x - 5})

What is the integral of ln(x+16) ?
The integral of ln(x+16) is xln(x+16)+16ln(x+16)-x-16+C