What is the integral from 1 to 4 of (x/2-4/x) ?

The integral from 1 to 4 of (x/2-4/x) is 15/4-8ln(2)

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integral from 1 to 4 of (x/2-4/x)

\int_{1}^{4} (\frac{x}{2} - \frac{4}{x}) d x

\frac{15}{4} - 8 ln (2)

Decimal

- 1.79517 \dots

Solution steps

\int_{1}^{4} \frac{x}{2} - \frac{4}{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}^{4} \frac{x}{2} d x - \int_{1}^{4} \frac{4}{x} d x

\int_{1}^{4} \frac{x}{2} d x = \frac{15}{4}

\int_{1}^{4} \frac{4}{x} d x = 8 ln (2)

= \frac{15}{4} - 8 ln (2)

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What is the integral from 1 to 4 of (x/2-4/x) ?
The integral from 1 to 4 of (x/2-4/x) is 15/4-8ln(2)