integral of (8x^{3/5}-3x^{-4}+4)

解

\int (8 x^{\frac{3}{5}} - 3 x^{- 4} + 4) d x

5 x^{\frac{8}{5}} + \frac{1}{x ^{3}} + 4 x + C

解答ステップ

\int 8 x^{\frac{3}{5}} - 3 x^{- 4} + 4 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^{\frac{3}{5}} d x - \int 3 x^{- 4} d x + \int 4 d x

\int 8 x^{\frac{3}{5}} d x = 5 x^{\frac{8}{5}}

\int 3 x^{- 4} d x = - \frac{1}{x ^{3}}

\int 4 d x = 4 x

= 5 x^{\frac{8}{5}} - (- \frac{1}{x ^{3}}) + 4 x

簡素化

= 5 x^{\frac{8}{5}} + \frac{1}{x ^{3}} + 4 x

定数を解答に追加する

= 5 x^{\frac{8}{5}} + \frac{1}{x ^{3}} + 4 x + C