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

The integral of (((ln(x))^2)/x) is (ln^3(x))/3+C

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

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

\frac{ln ^{3} ( x )}{3} + C

Solution steps

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

Apply u-substitution

: \int u^{2} d u

= \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= \frac{u ^{3}}{3}

Substitute back

u = ln (x)

= \frac{ln ^{3} ( x )}{3}

Add a constant to the solution

= \frac{ln ^{3} ( x )}{3} + C

\int cos^{3} (u) d u

x \to π lim (cos (3 x))

\frac{d}{d x} (2 x 64 - x^{2})

x \to - 1 lim (- 1^{3})

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

What is the integral of (((ln(x))^2)/x) ?
The integral of (((ln(x))^2)/x) is (ln^3(x))/3+C