What is the integral of (ln^4(x))/x ?

The integral of (ln^4(x))/x is (ln^5(x))/5+C

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integral of (ln^4(x))/x

\int \frac{ln ^{4} ( x )}{x} d x

\frac{ln ^{5} ( x )}{5} + C

Solution steps

\int \frac{ln ^{4} ( x )}{x} d x

Apply u-substitution

= \int u^{4} d u

Apply the Power Rule

= \frac{u ^{5}}{5}

Substitute back

u = ln (x)

= \frac{ln ^{5} ( x )}{5}

Add a constant to the solution

= \frac{ln ^{5} ( x )}{5} + C

What is the integral of (ln^4(x))/x ?
The integral of (ln^4(x))/x is (ln^5(x))/5+C