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

解答

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

2585

求解步骤

\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

使用积分加法定则:

\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

化简

= 2585

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