What is the integral from 2 to 3 of (ln(x))/x ?

The integral from 2 to 3 of (ln(x))/x is (ln^2(3)-ln^2(2))/2

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integral from 2 to 3 of (ln(x))/x

\int_{2}^{3} \frac{ln ( x )}{x} d x

\frac{ln ^{2} ( 3 ) - ln ^{2} ( 2 )}{2}

Decimal

0.36324 \dots

Solution steps

\int_{2}^{3} \frac{ln ( x )}{x} d x

Apply u-substitution

: \int_{l n (2)}^{l n (3)} u d u

= \int_{l n (2)}^{l n (3)} u d u

Apply the Power Rule

: [\frac{u ^{2}}{2}]_{l n (2)}^{l n (3)}

= [\frac{u ^{2}}{2}]_{l n (2)}^{l n (3)}

Compute the boundaries:

\frac{ln ^{2} ( 3 ) - ln ^{2} ( 2 )}{2}

= \frac{ln ^{2} ( 3 ) - ln ^{2} ( 2 )}{2}

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What is the integral from 2 to 3 of (ln(x))/x ?
The integral from 2 to 3 of (ln(x))/x is (ln^2(3)-ln^2(2))/2