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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int u^{5} d u

= \int u^{5} d u

Apply the Power Rule

: \frac{u ^{6}}{6}

= \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

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