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

integral

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

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

Solution steps

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

Apply u-substitution

= \int u^{3} d u

Apply the Power Rule

= \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

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