What is the integral from 1 to 3 of (2x^3-9x^{-2}) ?

The integral from 1 to 3 of (2x^3-9x^{-2}) is 34

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integral from 1 to 3 of (2x^3-9x^{-2})

\int_{1}^{3} (2 x^{3} - 9 x^{- 2}) d x

34

Solution steps

\int_{1}^{3} 2 x^{3} - 9 x^{- 2} d x

9 x^{- 2} = \frac{9}{x ^{2}}

= \int_{1}^{3} 2 x^{3} - \frac{9}{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_{1}^{3} 2 x^{3} d x - \int_{1}^{3} \frac{9}{x ^{2}} d x

\int_{1}^{3} 2 x^{3} d x = 40

\int_{1}^{3} \frac{9}{x ^{2}} d x = 6

= 40 - 6

Simplify

= 34

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What is the integral from 1 to 3 of (2x^3-9x^{-2}) ?
The integral from 1 to 3 of (2x^3-9x^{-2}) is 34