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

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

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

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

\frac{1}{2}

Decimal Notation

0.5

Solution steps

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

Apply u-substitution

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

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{1}{2}

= \frac{1}{2}

(1 + 6 x^{2}) (x - x^{2})

x \to \infty lim (- 3 x^{2})

y^{^{''}} - 2 y^{^{'}} - 3 y = 0, y (0) = b, y^{^{'}} (0) = 2

\frac{\partial}{\partial x} (cos (2 (2 y x - 1)))

\frac{\partial}{\partial x} (e^{x yz - 2})

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