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

The integral from-3 to-1 of 1/(x^2)-1/(x^3) is 10/9

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

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

\frac{10}{9}

Decimal

1.11111 \dots

Solution steps

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

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

\int_{- 3}^{- 1} \frac{1}{x ^{3}} d x = - \frac{4}{9}

= \frac{2}{3} - (- \frac{4}{9})

Simplify

\frac{2}{3} - (- \frac{4}{9}) : \frac{10}{9}

= \frac{10}{9}

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What is the integral from-3 to-1 of 1/(x^2)-1/(x^3) ?
The integral from-3 to-1 of 1/(x^2)-1/(x^3) is 10/9