What is the integral from 1 to 8 of 8/x-x/8 ?

The integral from 1 to 8 of 8/x-x/8 is 24ln(2)-63/16

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integral from 1 to 8 of 8/x-x/8

\int_{1}^{8} \frac{8}{x} - \frac{x}{8} d x

24 ln (2) - \frac{63}{16}

Decimal

12.69803 \dots

Solution steps

\int_{1}^{8} \frac{8}{x} - \frac{x}{8} 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}^{8} \frac{8}{x} d x - \int_{1}^{8} \frac{x}{8} d x

\int_{1}^{8} \frac{8}{x} d x = 24 ln (2)

\int_{1}^{8} \frac{x}{8} d x = \frac{63}{16}

= 24 ln (2) - \frac{63}{16}

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What is the integral from 1 to 8 of 8/x-x/8 ?
The integral from 1 to 8 of 8/x-x/8 is 24ln(2)-63/16