What is the integral from 1 to e^4 of (ln(x))/x ?

The integral from 1 to e^4 of (ln(x))/x is 8

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integral from 1 to e^4 of (ln(x))/x

\int_{1}^{e^{4}} \frac{ln ( x )}{x} d x

8

Solution steps

\int_{1}^{e^{4}} \frac{ln ( x )}{x} d x

Apply u-substitution

: \int_{0}^{4} u d u

= \int_{0}^{4} u d u

Apply the Power Rule

: [\frac{u ^{2}}{2}]_{0}^{4}

= [\frac{u ^{2}}{2}]_{0}^{4}

Compute the boundaries:

8

= 8

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What is the integral from 1 to e^4 of (ln(x))/x ?
The integral from 1 to e^4 of (ln(x))/x is 8