What is the integral of ((ln(x))^{18})/x ?

The integral of ((ln(x))^{18})/x is (ln^{19}(x))/(19)+C

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integral of ((ln(x))^{18})/x

\int \frac{( ln ( x ) ) ^{18}}{x} d x

\frac{ln ^{19} ( x )}{19} + C

Solution steps

\int \frac{( ln ( x ) ) ^{18}}{x} d x

Apply u-substitution

: \int u^{18} d u

= \int u^{18} d u

Apply the Power Rule

: \frac{u ^{19}}{19}

= \frac{u ^{19}}{19}

Substitute back

u = ln (x)

= \frac{ln ^{19} ( x )}{19}

Add a constant to the solution

= \frac{ln ^{19} ( x )}{19} + C

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What is the integral of ((ln(x))^{18})/x ?
The integral of ((ln(x))^{18})/x is (ln^{19}(x))/(19)+C