integral of x^7-1/(x^7)

解

\int x^{7} - \frac{1}{x ^{7}} d x

\frac{x ^{8}}{8} + \frac{1}{6 x ^{6}} + C

解答ステップ

\int x^{7} - \frac{1}{x ^{7}} 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^{7} d x - \int \frac{1}{x ^{7}} d x

\int x^{7} d x = \frac{x ^{8}}{8}

\int \frac{1}{x ^{7}} d x = - \frac{1}{6 x ^{6}}

= \frac{x ^{8}}{8} - (- \frac{1}{6 x ^{6}})

簡素化

= \frac{x ^{8}}{8} + \frac{1}{6 x ^{6}}

定数を解答に追加する

= \frac{x ^{8}}{8} + \frac{1}{6 x ^{6}} + C