What is the integral of ((ln(x))^{13})/x ?

The integral of ((ln(x))^{13})/x is (ln^{14}(x))/(14)+C

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integral of ((ln(x))^{13})/x

\int \frac{( ln ( x ) ) ^{13}}{x} d x

\frac{ln ^{14} ( x )}{14} + C

Solution steps

\int \frac{( ln ( x ) ) ^{13}}{x} d x

Simplify

= \int \frac{ln ^{13} ( x )}{x} d x

Apply u-substitution

= \int u^{13} d u

Apply the Power Rule

= \frac{u ^{14}}{14}

Substitute back

u = ln (x)

= \frac{ln ^{14} ( x )}{14}

Add a constant to the solution

= \frac{ln ^{14} ( x )}{14} + C

What is the integral of ((ln(x))^{13})/x ?
The integral of ((ln(x))^{13})/x is (ln^{14}(x))/(14)+C