integral of 8x^{1/3}+8x^{-1/3}

解

\int 8 x^{\frac{1}{3}} + 8 x^{- \frac{1}{3}} d x

6 x^{\frac{4}{3}} + 12 x^{\frac{2}{3}} + C

解答ステップ

\int 8 x^{\frac{1}{3}} + 8 x^{- \frac{1}{3}} 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{1}{3}} d x + \int 8 x^{- \frac{1}{3}} d x

\int 8 x^{\frac{1}{3}} d x = 6 x^{\frac{4}{3}}

\int 8 x^{- \frac{1}{3}} d x = 12 x^{\frac{2}{3}}

= 6 x^{\frac{4}{3}} + 12 x^{\frac{2}{3}}

定数を解答に追加する

= 6 x^{\frac{4}{3}} + 12 x^{\frac{2}{3}} + C