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

解

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

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

解答ステップ

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

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

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

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

定数を解答に追加する

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