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

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

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integral from 1 to 2 of (ln(2x))/x

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

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

Decimal

0.72067 \dots

Solution steps

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

Apply u-substitution

: \int_{2}^{4} \frac{ln ( u )}{u} d u

= \int_{2}^{4} \frac{ln ( u )}{u} d u

Apply u-substitution

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

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

Apply the Power Rule

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

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

Compute the boundaries:

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

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

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