What is the integral from 1 to e of (((ln(x))^5))/x ?

The integral from 1 to e of (((ln(x))^5))/x is 1/6

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integral from 1 to e of (((ln(x))^5))/x

\int_{1}^{e} \frac{( ( ln ( x ) ) ^{5} )}{x} d x

\frac{1}{6}

Decimal

0.16666 \dots

Solution steps

\int_{1}^{e} \frac{( ln ( x ) ) ^{5}}{x} d x

Apply u-substitution

= \int_{0}^{1} u^{5} d u

Apply the Power Rule

= [\frac{u ^{6}}{6}]_{0}^{1}

Compute the boundaries:

\frac{1}{6}

= \frac{1}{6}

What is the integral from 1 to e of (((ln(x))^5))/x ?
The integral from 1 to e of (((ln(x))^5))/x is 1/6