integral of (2x^2+7x^{-2})

解答

\int (2 x^{2} + 7 x^{- 2}) d x

\frac{2 x ^{3}}{3} - \frac{7}{x} + C

求解步骤

\int 2 x^{2} + 7 x^{- 2} d x

7 x^{- 2} = \frac{7}{x ^{2}}

= \int 2 x^{2} + \frac{7}{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 2 x^{2} d x + \int \frac{7}{x ^{2}} d x

\int 2 x^{2} d x = \frac{2 x ^{3}}{3}

\int \frac{7}{x ^{2}} d x = - \frac{7}{x}

= \frac{2 x ^{3}}{3} - \frac{7}{x}

解答补常数

= \frac{2 x ^{3}}{3} - \frac{7}{x} + C

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