What is the integral from 5 to 8 of (5/(x^2)-1) ?

The integral from 5 to 8 of (5/(x^2)-1) is -21/8

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integral from 5 to 8 of (5/(x^2)-1)

\int_{5}^{8} (\frac{5}{x ^{2}} - 1) d x

- \frac{21}{8}

Decimal

- 2.625

Solution steps

\int_{5}^{8} \frac{5}{x ^{2}} - 1 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_{5}^{8} \frac{5}{x ^{2}} d x - \int_{5}^{8} 1 d x

\int_{5}^{8} \frac{5}{x ^{2}} d x = \frac{3}{8}

\int_{5}^{8} 1 d x = 3

= \frac{3}{8} - 3

Simplify

\frac{3}{8} - 3 : - \frac{21}{8}

= - \frac{21}{8}

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What is the integral from 5 to 8 of (5/(x^2)-1) ?
The integral from 5 to 8 of (5/(x^2)-1) is -21/8