What is the integral from 8 to 10 of x/8-8/x ?

The integral from 8 to 10 of x/8-8/x is 9/4-8ln(5/4)

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integral from 8 to 10 of x/8-8/x

\int_{8}^{10} \frac{x}{8} - \frac{8}{x} d x

\frac{9}{4} - 8 ln (\frac{5}{4})

Decimal

0.46485 \dots

Solution steps

\int_{8}^{10} \frac{x}{8} - \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_{8}^{10} \frac{x}{8} d x - \int_{8}^{10} \frac{8}{x} d x

\int_{8}^{10} \frac{x}{8} d x = \frac{9}{4}

\int_{8}^{10} \frac{8}{x} d x = 8 ln (\frac{5}{4})

= \frac{9}{4} - 8 ln (\frac{5}{4})

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What is the integral from 8 to 10 of x/8-8/x ?
The integral from 8 to 10 of x/8-8/x is 9/4-8ln(5/4)