integral of \sqrt[9]{x}+1/(\sqrt[9]{x)}

解

\int 9 x + \frac{1}{9 x} d x

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

解答ステップ

\int 9 x + \frac{1}{9 x} 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 9 x d x + \int \frac{1}{9 x} d x

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

\int \frac{1}{9 x} d x = \frac{9}{8} x^{\frac{8}{9}}

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

定数を解答に追加する

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