integral of (8x^7-7/(x^7))

解

\int (8 x^{7} - \frac{7}{x ^{7}}) d x

x^{8} + \frac{7}{6 x ^{6}} + C

解答ステップ

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

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

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

= x^{8} - (- \frac{7}{6 x ^{6}})

簡素化

= x^{8} + \frac{7}{6 x ^{6}}

定数を解答に追加する

= x^{8} + \frac{7}{6 x ^{6}} + C