integral of (3x^{-2}-4x^{-3})

解答

\int (3 x^{- 2} - 4 x^{- 3}) d x

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

求解步骤

\int 3 x^{- 2} - 4 x^{- 3} d x

化简

3 x^{- 2} - 4 x^{- 3} : \frac{3}{x ^{2}} - \frac{4}{x ^{3}}

= \int \frac{3}{x ^{2}} - \frac{4}{x ^{3}} 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 \frac{3}{x ^{2}} d x - \int \frac{4}{x ^{3}} d x

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

\int \frac{4}{x ^{3}} d x = - \frac{2}{x ^{2}}

= - \frac{3}{x} - (- \frac{2}{x ^{2}})

化简

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

解答补常数

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

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