What is the integral from 1 to 4 of (x/8-7/x) ?

The integral from 1 to 4 of (x/8-7/x) is 15/16-14ln(2)

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integral from 1 to 4 of (x/8-7/x)

\int_{1}^{4} (\frac{x}{8} - \frac{7}{x}) d x

\frac{15}{16} - 14 ln (2)

Decimal

- 8.76656 \dots

Solution steps

\int_{1}^{4} \frac{x}{8} - \frac{7}{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}{8} d x - \int_{1}^{4} \frac{7}{x} d x

\int_{1}^{4} \frac{x}{8} d x = \frac{15}{16}

\int_{1}^{4} \frac{7}{x} d x = 14 ln (2)

= \frac{15}{16} - 14 ln (2)

\int_{0}^{\frac{π}{2}} \frac{1}{2} d x

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What is the integral from 1 to 4 of (x/8-7/x) ?
The integral from 1 to 4 of (x/8-7/x) is 15/16-14ln(2)