What is the integral from 1 to 8 of (ln(x))/x ?

The integral from 1 to 8 of (ln(x))/x is (9ln^2(2))/2

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integral from 1 to 8 of (ln(x))/x

\int_{1}^{8} \frac{ln ( x )}{x} d x

\frac{9 ln ^{2} ( 2 )}{2}

Decimal

2.16203 \dots

Solution steps

\int_{1}^{8} \frac{ln ( x )}{x} d x

Apply u-substitution

: \int_{0}^{3 l n (2)} u d u

= \int_{0}^{3 l n (2)} u d u

Apply the Power Rule

: [\frac{u ^{2}}{2}]_{0}^{3 l n (2)}

= [\frac{u ^{2}}{2}]_{0}^{3 l n (2)}

Compute the boundaries:

\frac{9 ln ^{2} ( 2 )}{2}

= \frac{9 ln ^{2} ( 2 )}{2}

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What is the integral from 1 to 8 of (ln(x))/x ?
The integral from 1 to 8 of (ln(x))/x is (9ln^2(2))/2