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

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

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

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

0

Solution steps

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

Apply u-substitution

: \int_{- l n (x)}^{l n (x)} u d u

= \int_{- l n (x)}^{l n (x)} u d u

Apply the Power Rule

: [\frac{u ^{2}}{2}]_{- l n (x)}^{l n (x)}

= [\frac{u ^{2}}{2}]_{- l n (x)}^{l n (x)}

Compute the boundaries:

\frac{ln ^{2} ( x )}{2} - \frac{1}{2} ln^{2} (x)

= \frac{ln ^{2} ( x )}{2} - \frac{1}{2} ln^{2} (x)

Simplify

= 0

\int_{1}^{3} - x^{2} + 4 x d x

\int_{0}^{l n (3)} e^{x - e^{x}} d x

\int_{- 4}^{4} (x^{2} - 16) d x

\int_{0}^{1} \frac{x + 5}{x ^{2} + 5 x + 6} d x

\int_{0}^{2} (x) (x) d x

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