What is the integral of (ln(x+5))/(x+5) ?

The integral of (ln(x+5))/(x+5) is (ln^2(x+5))/2+C

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integral of (ln(x+5))/(x+5)

\int \frac{ln ( x + 5 )}{x + 5} d x

\frac{ln ^{2} ( x + 5 )}{2} + C

Solution steps

\int \frac{ln ( x + 5 )}{x + 5} 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 + 5 )}{2}

Add a constant to the solution

= \frac{ln ^{2} ( x + 5 )}{2} + C

\frac{\partial}{\partial t} (2)

\frac{d y}{d x} + y^{2} = 0

x \to 3 lim (\frac{2 ^{x} - 8}{x - 3})

\int \frac{8}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x

f (x) = \frac{5}{x}

What is the integral of (ln(x+5))/(x+5) ?
The integral of (ln(x+5))/(x+5) is (ln^2(x+5))/2+C