integral of ((1-2x^3)/(x^3))

解

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

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

解答ステップ

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

拡張

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

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

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

\int 2 d x = 2 x

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

定数を解答に追加する

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