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

x \to \infty lim (6 x^{4})

y = 2 x (x + 1)^{2}, (0, 0)

\int 3 x^{2} + 6 x + 5 d x

\frac{\partial}{\partial y} (z^{3} - x^{2} y)

(x cos (x))^{^{'}}

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