What is the integral from 1 to 8 of (x/2-9/x) ?

The integral from 1 to 8 of (x/2-9/x) is 63/4-27ln(2)

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integral from 1 to 8 of (x/2-9/x)

\int_{1}^{8} (\frac{x}{2} - \frac{9}{x}) d x

\frac{63}{4} - 27 ln (2)

Decimal

- 2.96497 \dots

Solution steps

\int_{1}^{8} \frac{x}{2} - \frac{9}{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}^{8} \frac{x}{2} d x - \int_{1}^{8} \frac{9}{x} d x

\int_{1}^{8} \frac{x}{2} d x = \frac{63}{4}

\int_{1}^{8} \frac{9}{x} d x = 27 ln (2)

= \frac{63}{4} - 27 ln (2)

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What is the integral from 1 to 8 of (x/2-9/x) ?
The integral from 1 to 8 of (x/2-9/x) is 63/4-27ln(2)