What is the integral of ([ln(x)]^3)/x ?

The integral of ([ln(x)]^3)/x is (ln^4(x))/4+C

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integral of ([ln(x)]^3)/x

\int \frac{[ ln ( x ) ] ^{3}}{x} d x

\frac{ln ^{4} ( x )}{4} + C

Solution steps

\int \frac{[ ln ( x ) ] ^{3}}{x} d x

Simplify

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

Apply u-substitution

: \int u^{3} d u

= \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

= \frac{u ^{4}}{4}

Substitute back

u = ln (x)

= \frac{ln ^{4} ( x )}{4}

Add a constant to the solution

= \frac{ln ^{4} ( x )}{4} + C

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What is the integral of ([ln(x)]^3)/x ?
The integral of ([ln(x)]^3)/x is (ln^4(x))/4+C