What is the integral of ((ln(x))^{40})/x ?

The integral of ((ln(x))^{40})/x is (ln^{41}(x))/(41)+C

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integral of ((ln(x))^{40})/x

\int \frac{( ln ( x ) ) ^{40}}{x} d x

\frac{ln ^{41} ( x )}{41} + C

Solution steps

\int \frac{( ln ( x ) ) ^{40}}{x} d x

Apply u-substitution

: \int u^{40} d u

= \int u^{40} d u

Apply the Power Rule

: \frac{u ^{41}}{41}

= \frac{u ^{41}}{41}

Substitute back

u = ln (x)

= \frac{ln ^{41} ( x )}{41}

Add a constant to the solution

= \frac{ln ^{41} ( x )}{41} + C

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What is the integral of ((ln(x))^{40})/x ?
The integral of ((ln(x))^{40})/x is (ln^{41}(x))/(41)+C