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

The integral of (ln(x+2))/(x+2) is (ln^2(x+2))/2+C

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integral of (ln(x+2))/(x+2)

\int \frac{ln ( x + 2 )}{x + 2} d x

\frac{ln ^{2} ( x + 2 )}{2} + C

Solution steps

\int \frac{ln ( x + 2 )}{x + 2} d x

Apply u-substitution

: \int \frac{ln ( u )}{u} d u

= \int \frac{ln ( u )}{u} d u

Apply u-substitution

: \int v d v

= \int v d v

Apply the Power Rule

: \frac{v ^{2}}{2}

= \frac{v ^{2}}{2}

Substitute back

= \frac{ln ^{2} ( x + 2 )}{2}

Add a constant to the solution

= \frac{ln ^{2} ( x + 2 )}{2} + C

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

\frac{1}{3 + t}

\int e^{- a \cdot x^{2}} d x

f (x) = 5 cos (x)

\frac{d}{d x} (\frac{0.25 e ^{x}}{1 - 0.75 e ^{x}})

What is the integral of (ln(x+2))/(x+2) ?
The integral of (ln(x+2))/(x+2) is (ln^2(x+2))/2+C