What is the integral from-3 to-1 of ((x^5-2x)/(x^3)) ?

The integral from-3 to-1 of ((x^5-2x)/(x^3)) is 22/3

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integral from-3 to-1 of ((x^5-2x)/(x^3))

\int_{- 3}^{- 1} (\frac{x ^{5} - 2 x}{x ^{3}}) d x

\frac{22}{3}

Decimal

7.33333 \dots

Solution steps

\int_{- 3}^{- 1} \frac{x ^{5} - 2 x}{x ^{3}} d x

Expand

\frac{x ^{5} - 2 x}{x ^{3}} : x^{2} - \frac{2}{x ^{2}}

= \int_{- 3}^{- 1} x^{2} - \frac{2}{x ^{2}} 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_{- 3}^{- 1} x^{2} d x - \int_{- 3}^{- 1} \frac{2}{x ^{2}} d x

\int_{- 3}^{- 1} x^{2} d x = \frac{26}{3}

\int_{- 3}^{- 1} \frac{2}{x ^{2}} d x = \frac{4}{3}

= \frac{26}{3} - \frac{4}{3}

Simplify

\frac{26}{3} - \frac{4}{3} : \frac{22}{3}

= \frac{22}{3}

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What is the integral from-3 to-1 of ((x^5-2x)/(x^3)) ?
The integral from-3 to-1 of ((x^5-2x)/(x^3)) is 22/3