What is the integral of ln(x+3) ?

The integral of ln(x+3) is xln(x+3)+3ln(x+3)-x-3+C

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integral of ln(x+3)

\int ln (x + 3) d x

x ln (x + 3) + 3 ln (x + 3) - x - 3 + C

Solution steps

\int ln (x + 3) 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 + 3

= (x + 3) ln (x + 3) - (x + 3)

Simplify

(x + 3) ln (x + 3) - (x + 3) : x ln (x + 3) + 3 ln (x + 3) - x - 3

= x ln (x + 3) + 3 ln (x + 3) - x - 3

Add a constant to the solution

= x ln (x + 3) + 3 ln (x + 3) - x - 3 + C

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

y = 9 x - x^{2}, y = 2 x

\int x^{7} e^{- x^{8}} d x

y^{^{'}} + \frac{1}{x} y = x^{2} y^{1}

\int \frac{1}{3 ^{x}} d x

What is the integral of ln(x+3) ?
The integral of ln(x+3) is xln(x+3)+3ln(x+3)-x-3+C