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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int_{0}^{l n (x)} u d u

= \int_{0}^{l n (x)} u d u

Apply the Power Rule

: [\frac{u ^{2}}{2}]_{0}^{l n (x)}

= [\frac{u ^{2}}{2}]_{0}^{l n (x)}

Compute the boundaries:

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

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

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\int_{- 1}^{0} - 2 cos (\frac{nπ x}{2}) d x

\int_{0}^{1} 6 x y (2 - x - y) d x

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