integral of (\sqrt[4]{x}+\sqrt[5]{x})

解

\int (4 x + 5 x) d x

\frac{4}{5} x^{\frac{5}{4}} + \frac{5}{6} x^{\frac{6}{5}} + C

解答ステップ

\int 4 x + 5 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 4 x d x + \int 5 x d x

\int 4 x d x = \frac{4}{5} x^{\frac{5}{4}}

\int 5 x d x = \frac{5}{6} x^{\frac{6}{5}}

= \frac{4}{5} x^{\frac{5}{4}} + \frac{5}{6} x^{\frac{6}{5}}

定数を解答に追加する

= \frac{4}{5} x^{\frac{5}{4}} + \frac{5}{6} x^{\frac{6}{5}} + C