integral of (4-x)\sqrt[3]{x}

解答

\int (4 - x) 3 x d x

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

求解步骤

\int (4 - x) 3 x d x

乘开

(4 - x) 3 x : 4 3 x - x^{\frac{4}{3}}

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

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

\int x^{\frac{4}{3}} d x = \frac{3}{7} x^{\frac{7}{3}}

= 3 x^{\frac{4}{3}} - \frac{3}{7} x^{\frac{7}{3}}

解答补常数

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

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