integral of (1/(x^9)-x^9-1/8)

解

\int (\frac{1}{x ^{9}} - x^{9} - \frac{1}{8}) d x

- \frac{1}{8 x ^{8}} - \frac{x ^{10}}{10} - \frac{1}{8} x + C

解答ステップ

\int \frac{1}{x ^{9}} - x^{9} - \frac{1}{8} 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 ^{9}} d x - \int x^{9} d x - \int \frac{1}{8} d x

\int \frac{1}{x ^{9}} d x = - \frac{1}{8 x ^{8}}

\int x^{9} d x = \frac{x ^{10}}{10}

\int \frac{1}{8} d x = \frac{1}{8} x

= - \frac{1}{8 x ^{8}} - \frac{x ^{10}}{10} - \frac{1}{8} x

定数を解答に追加する

= - \frac{1}{8 x ^{8}} - \frac{x ^{10}}{10} - \frac{1}{8} x + C