What is the integral from 1 to 6 of 8x^3-6x^{-2} ?

The integral from 1 to 6 of 8x^3-6x^{-2} is 2585

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integral from 1 to 6 of 8x^3-6x^{-2}

\int_{1}^{6} 8 x^{3} - 6 x^{- 2} d x

2585

Solution steps

\int_{1}^{6} 8 x^{3} - 6 x^{- 2} d x

6 x^{- 2} = \frac{6}{x ^{2}}

= \int_{1}^{6} 8 x^{3} - \frac{6}{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}^{6} 8 x^{3} d x - \int_{1}^{6} \frac{6}{x ^{2}} d x

\int_{1}^{6} 8 x^{3} d x = 2590

\int_{1}^{6} \frac{6}{x ^{2}} d x = 5

= 2590 - 5

Simplify

= 2585

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\int_{1}^{e} in x d x

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What is the integral from 1 to 6 of 8x^3-6x^{-2} ?
The integral from 1 to 6 of 8x^3-6x^{-2} is 2585