integral of (7sqrt(x^3)+4\sqrt[3]{x^2})

解

\int (7 x^{3} + 4 3 x^{2}) d x

\frac{14}{5} x^{\frac{5}{2}} + \frac{12}{5} x^{\frac{5}{3}} + C

解答ステップ

\int 7 x^{3} + 4 3 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 7 x^{3} d x + \int 4 3 x^{2} d x

\int 7 x^{3} d x = \frac{14}{5} x^{\frac{5}{2}}

\int 4 3 x^{2} d x = \frac{12}{5} x^{\frac{5}{3}}

= \frac{14}{5} x^{\frac{5}{2}} + \frac{12}{5} x^{\frac{5}{3}}

定数を解答に追加する

= \frac{14}{5} x^{\frac{5}{2}} + \frac{12}{5} x^{\frac{5}{3}} + C