integral of 10x^9-9/(x^9)

解

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

x^{10} + \frac{9}{8 x ^{8}} + C

解答ステップ

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

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

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

= x^{10} - (- \frac{9}{8 x ^{8}})

簡素化

= x^{10} + \frac{9}{8 x ^{8}}

定数を解答に追加する

= x^{10} + \frac{9}{8 x ^{8}} + C