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

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

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

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

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

Solution steps

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

f (x) = 6 - x^{2}

\int \frac{7 + x}{x} d x

\frac{d}{d x} (x - cos (x))

\frac{d}{d x} ((x - 4) ln (\frac{x}{4}))

f (x) = x^{2} - 2

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