integral of (x^{5/9}-7x^{7/6})

解

\int (x^{\frac{5}{9}} - 7 x^{\frac{7}{6}}) d x

\frac{9}{14} x^{\frac{14}{9}} - \frac{42}{13} x^{\frac{13}{6}} + C

解答ステップ

\int x^{\frac{5}{9}} - 7 x^{\frac{7}{6}} 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 x^{\frac{5}{9}} d x - \int 7 x^{\frac{7}{6}} d x

\int x^{\frac{5}{9}} d x = \frac{9}{14} x^{\frac{14}{9}}

\int 7 x^{\frac{7}{6}} d x = \frac{42}{13} x^{\frac{13}{6}}

= \frac{9}{14} x^{\frac{14}{9}} - \frac{42}{13} x^{\frac{13}{6}}

定数を解答に追加する

= \frac{9}{14} x^{\frac{14}{9}} - \frac{42}{13} x^{\frac{13}{6}} + C