What is the integral of (((ln(x))^8))/x ?

The integral of (((ln(x))^8))/x is (ln^9(x))/9+C

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integral of (((ln(x))^8))/x

\int \frac{( ( ln ( x ) ) ^{8} )}{x} d x

\frac{ln ^{9} ( x )}{9} + C

Solution steps

\int \frac{( ln ( x ) ) ^{8}}{x} d x

Apply u-substitution

: \int u^{8} d u

= \int u^{8} d u

Apply the Power Rule

: \frac{u ^{9}}{9}

= \frac{u ^{9}}{9}

Substitute back

u = ln (x)

= \frac{ln ^{9} ( x )}{9}

Add a constant to the solution

= \frac{ln ^{9} ( x )}{9} + C

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What is the integral of (((ln(x))^8))/x ?
The integral of (((ln(x))^8))/x is (ln^9(x))/9+C