integral of (2-sqrt(x))/(x^2)

解答

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

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

求解步骤

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

乘开

\frac{2 - x}{x ^{2}} : \frac{2}{x ^{2}} - \frac{1}{x ^{\frac{3}{2}}}

= \int \frac{2}{x ^{2}} - \frac{1}{x ^{\frac{3}{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 \frac{2}{x ^{2}} d x - \int \frac{1}{x ^{\frac{3}{2}}} d x

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

\int \frac{1}{x ^{\frac{3}{2}}} d x = - \frac{2}{x}

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

化简

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

解答补常数

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

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