What is the integral of ln(x+2) ?

The integral of ln(x+2) is xln(x+2)+2ln(x+2)-x-2+C

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integral of ln(x+2)

integral

ln (x + 2)

x ln (x + 2) + 2 ln (x + 2) - x - 2 + C

Solution steps

\int ln (x + 2) 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 + 2

= (x + 2) ln (x + 2) - (x + 2)

Simplify

(x + 2) ln (x + 2) - (x + 2) : x ln (x + 2) + 2 ln (x + 2) - x - 2

= x ln (x + 2) + 2 ln (x + 2) - x - 2

Add a constant to the solution

= x ln (x + 2) + 2 ln (x + 2) - x - 2 + C

\frac{cos ^{2} ( x )}{2}

\frac{x}{( x + 1 )}

3 x^{3}

\frac{x}{( x ^{2} + y ^{2} )}

\frac{1}{( x ^{2} - a ^{2} )}

What is the integral of ln(x+2) ?
The integral of ln(x+2) is xln(x+2)+2ln(x+2)-x-2+C