integral of (3\sqrt[5]{x^2}-sqrt(x)+2)

解

\int (3 5 x^{2} - x + 2) d x

\frac{15}{7} x^{\frac{7}{5}} - \frac{2}{3} x^{\frac{3}{2}} + 2 x + C

解答ステップ

\int 3 5 x^{2} - x + 2 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 3 5 x^{2} d x - \int x d x + \int 2 d x

\int 3 5 x^{2} d x = \frac{15}{7} x^{\frac{7}{5}}

\int x d x = \frac{2}{3} x^{\frac{3}{2}}

\int 2 d x = 2 x

= \frac{15}{7} x^{\frac{7}{5}} - \frac{2}{3} x^{\frac{3}{2}} + 2 x

定数を解答に追加する

= \frac{15}{7} x^{\frac{7}{5}} - \frac{2}{3} x^{\frac{3}{2}} + 2 x + C