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

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

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integral of ((ln(x)))/x

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

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

Solution steps

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

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= \frac{u ^{2}}{2}

Substitute back

u = ln (x)

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

Add a constant to the solution

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

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

x \to 0 lim (\frac{arcsin ( 3 x )}{x})

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

- \frac{1}{5} x^{2} - \frac{6}{5} x + \frac{7}{5}, [- 5, 5]

y^{^{'}} = 24.5 - \frac{7 y}{( 280 - 2 x )}

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