integral of (x-1/(x^2))

解

\int (x - \frac{1}{x ^{2}}) d x

\frac{x ^{2}}{2} + \frac{1}{x} + C

解答ステップ

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

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

= \frac{x ^{2}}{2} - (- \frac{1}{x})

簡素化

= \frac{x ^{2}}{2} + \frac{1}{x}

定数を解答に追加する

= \frac{x ^{2}}{2} + \frac{1}{x} + C