What is the integral of 1/x*ln(x) ?

The integral of 1/x*ln(x) is (ln^2(x))/2+C

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integral of 1/x*ln(x)

\int \frac{1}{x} \cdot ln (x) d x

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

Solution steps

\int \frac{1}{x} ln (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 w d w

\frac{d}{d x} (6 x^{2} + 4)

\frac{\partial}{\partial x} (ln (x - 8 y))