What is the integral from 2 to 4 of 2x-8/x ?

The integral from 2 to 4 of 2x-8/x is 12-8ln(2)

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integral from 2 to 4 of 2x-8/x

\int_{2}^{4} 2 x - \frac{8}{x} d x

12 - 8 ln (2)

Decimal

6.45482 \dots

Solution steps

\int_{2}^{4} 2 x - \frac{8}{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_{2}^{4} 2 x d x - \int_{2}^{4} \frac{8}{x} d x

\int_{2}^{4} 2 x d x = 12

\int_{2}^{4} \frac{8}{x} d x = 8 ln (2)

= 12 - 8 ln (2)

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What is the integral from 2 to 4 of 2x-8/x ?
The integral from 2 to 4 of 2x-8/x is 12-8ln(2)