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

The integral from 1 to e of (sqrt(ln(x)))/x is 2/3

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integral from 1 to e of (sqrt(ln(x)))/x

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

\frac{2}{3}

Decimal

0.66666 \dots

Solution steps

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

Apply u-substitution

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

Apply the Power Rule

= [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{1}

Compute the boundaries:

\frac{2}{3}

= \frac{2}{3}

What is the integral from 1 to e of (sqrt(ln(x)))/x ?
The integral from 1 to e of (sqrt(ln(x)))/x is 2/3