integral of 4-7x^2+\sqrt[5]{x}

解

\int 4 - 7 x^{2} + 5 x d x

4 x - \frac{7 x ^{3}}{3} + \frac{5}{6} x^{\frac{6}{5}} + C

解答ステップ

\int 4 - 7 x^{2} + 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 d x - \int 7 x^{2} d x + \int 5 x d x

\int 4 d x = 4 x

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

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

= 4 x - \frac{7 x ^{3}}{3} + \frac{5}{6} x^{\frac{6}{5}}

定数を解答に追加する

= 4 x - \frac{7 x ^{3}}{3} + \frac{5}{6} x^{\frac{6}{5}} + C