What is the integral of ((ln^5(x)))/x ?

The integral of ((ln^5(x)))/x is (ln^6(x))/6+C

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integral of ((ln^5(x)))/x

\int \frac{( ln ^{5} ( x ) )}{x} d x

\frac{ln ^{6} ( x )}{6} + C

Solution steps

\int \frac{ln ^{5} ( x )}{x} d x

Apply u-substitution

= \int u^{5} d u

Apply the Power Rule

= \frac{u ^{6}}{6}

Substitute back

u = ln (x)

= \frac{ln ^{6} ( x )}{6}

Add a constant to the solution

= \frac{ln ^{6} ( x )}{6} + C

What is the integral of ((ln^5(x)))/x ?
The integral of ((ln^5(x)))/x is (ln^6(x))/6+C