integral of (4sin(x)-1+8x^{-5})

解

\int (4 sin (x) - 1 + 8 x^{- 5}) d x

- 4 cos (x) - x - \frac{2}{x ^{4}} + C

解答ステップ

\int 4 sin (x) - 1 + 8 x^{- 5} d x

8 x^{- 5} = \frac{8}{x ^{5}}

= \int 4 sin (x) - 1 + \frac{8}{x ^{5}} 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 4 sin (x) d x - \int 1 d x + \int \frac{8}{x ^{5}} d x

\int 4 sin (x) d x = - 4 cos (x)

\int 1 d x = x

\int \frac{8}{x ^{5}} d x = - \frac{2}{x ^{4}}

= - 4 cos (x) - x - \frac{2}{x ^{4}}

定数を解答に追加する

= - 4 cos (x) - x - \frac{2}{x ^{4}} + C