integral of-4x^{3/2}+3x^{2/3}-4x^2

解

\int - 4 x^{\frac{3}{2}} + 3 x^{\frac{2}{3}} - 4 x^{2} d x

- \frac{8}{5} x^{\frac{5}{2}} + \frac{9}{5} x^{\frac{5}{3}} - \frac{4 x ^{3}}{3} + C

解答ステップ

\int - 4 x^{\frac{3}{2}} + 3 x^{\frac{2}{3}} - 4 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 4 x^{\frac{3}{2}} d x + \int 3 x^{\frac{2}{3}} d x - \int 4 x^{2} d x

\int 4 x^{\frac{3}{2}} d x = \frac{8}{5} x^{\frac{5}{2}}

\int 3 x^{\frac{2}{3}} d x = \frac{9}{5} x^{\frac{5}{3}}

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

= - \frac{8}{5} x^{\frac{5}{2}} + \frac{9}{5} x^{\frac{5}{3}} - \frac{4 x ^{3}}{3}

定数を解答に追加する

= - \frac{8}{5} x^{\frac{5}{2}} + \frac{9}{5} x^{\frac{5}{3}} - \frac{4 x ^{3}}{3} + C