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

\int 0.25 e^{- 0.25 x} d x

\int e^{2 x^{4}} d x

\int_{1}^{8} \frac{1}{x - 3} d x

sin (π x)

\frac{d}{d x} (\frac{3 + 2 x - x ^{3}}{6})

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