integral of \sqrt[3]{w}+10\sqrt[5]{w^3}

解

\int 3 w + 10 5 w^{3} d w

\frac{3}{4} w^{\frac{4}{3}} + \frac{25}{4} w^{\frac{8}{5}} + C

解答ステップ

\int 3 w + 10 5 w^{3} d w

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 3 w d w + \int 10 5 w^{3} d w

\int 3 w d w = \frac{3}{4} w^{\frac{4}{3}}

\int 10 5 w^{3} d w = \frac{25}{4} w^{\frac{8}{5}}

= \frac{3}{4} w^{\frac{4}{3}} + \frac{25}{4} w^{\frac{8}{5}}

定数を解答に追加する

= \frac{3}{4} w^{\frac{4}{3}} + \frac{25}{4} w^{\frac{8}{5}} + C