What is the integral from 1 to 5 of ln(2x)-ln(x) ?

The integral from 1 to 5 of ln(2x)-ln(x) is ln(50000)-5ln(5)

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integral from 1 to 5 of ln(2x)-ln(x)

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

ln (50000) - 5 ln (5)

Decimal

2.77258 \dots

Solution steps

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

\int_{1}^{5} ln (2 x) d x = ln (50000) - 4

\int_{1}^{5} ln (x) d x = 5 ln (5) - 4

= ln (50000) - 4 - (5 ln (5) - 4)

Simplify

= ln (50000) - 5 ln (5)

What is the integral from 1 to 5 of ln(2x)-ln(x) ?
The integral from 1 to 5 of ln(2x)-ln(x) is ln(50000)-5ln(5)