What is the integral from 1 to 6 of ln(2x)-ln(x) ?

The integral from 1 to 6 of ln(2x)-ln(x) is ln(1492992)-6ln(6)

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integral from 1 to 6 of ln(2x)-ln(x)

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

ln (1492992) - 6 ln (6)

Decimal

3.46573 \dots

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{6} ln (2 x) d x - \int_{1}^{6} ln (x) d x

\int_{1}^{6} ln (2 x) d x = ln (1492992) - 5

\int_{1}^{6} ln (x) d x = 6 ln (6) - 5

= ln (1492992) - 5 - (6 ln (6) - 5)

Simplify

= ln (1492992) - 6 ln (6)

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What is the integral from 1 to 6 of ln(2x)-ln(x) ?
The integral from 1 to 6 of ln(2x)-ln(x) is ln(1492992)-6ln(6)