What is the integral of (((ln(x))^6))/x ?

The integral of (((ln(x))^6))/x is (ln^7(x))/7+C

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integral of (((ln(x))^6))/x

\int \frac{( ( ln ( x ) ) ^{6} )}{x} d x

\frac{ln ^{7} ( x )}{7} + C

Solution steps

\int \frac{( ln ( x ) ) ^{6}}{x} d x

Apply u-substitution

: \int u^{6} d u

= \int u^{6} d u

Apply the Power Rule

: \frac{u ^{7}}{7}

= \frac{u ^{7}}{7}

Substitute back

u = ln (x)

= \frac{ln ^{7} ( x )}{7}

Add a constant to the solution

= \frac{ln ^{7} ( x )}{7} + C

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What is the integral of (((ln(x))^6))/x ?
The integral of (((ln(x))^6))/x is (ln^7(x))/7+C