What is the integral of (((ln(x))^9)/x) ?

The integral of (((ln(x))^9)/x) is (ln^{10}(x))/(10)+C

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integral of (((ln(x))^9)/x)

\int (\frac{( ln ( x ) ) ^{9}}{x}) d x

\frac{ln ^{10} ( x )}{10} + C

Solution steps

\int \frac{( ln ( x ) ) ^{9}}{x} d x

Apply u-substitution

: \int u^{9} d u

= \int u^{9} d u

Apply the Power Rule

: \frac{u ^{10}}{10}

= \frac{u ^{10}}{10}

Substitute back

u = ln (x)

= \frac{ln ^{10} ( x )}{10}

Add a constant to the solution

= \frac{ln ^{10} ( x )}{10} + C

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What is the integral of (((ln(x))^9)/x) ?
The integral of (((ln(x))^9)/x) is (ln^{10}(x))/(10)+C