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

The integral from 1/e to e of (ln(x))/x is 0

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

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

0

Solution steps

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

Apply u-substitution

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

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

Apply the Power Rule

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

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

Compute the boundaries:

0

= 0

\int_{0}^{1} \frac{1}{t} d t

\int_{- \infty}^{1} 0 d x

\int_{0}^{2} \frac{2 t}{1 + t ^{2}} d t

\int_{- 3}^{4} - x^{2} + x + 12 d x

\int_{- 2}^{3} (3 x^{2} - 4 x) d x

What is the integral from 1/e to e of (ln(x))/x ?
The integral from 1/e to e of (ln(x))/x is 0