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

解

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

\frac{x ^{3}}{6} + \frac{2}{x} + C

解答ステップ

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

\int \frac{x ^{2}}{2} d x = \frac{x ^{3}}{6}

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

= \frac{x ^{3}}{6} - (- \frac{2}{x})

簡素化

= \frac{x ^{3}}{6} + \frac{2}{x}

定数を解答に追加する

= \frac{x ^{3}}{6} + \frac{2}{x} + C