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

Simplify

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

Apply u-substitution

= \int u^{2} d u

Apply the Power Rule

= \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

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