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

解答

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

- \frac{3}{25} x^{\frac{5}{3}} + C

求解步骤

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

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \frac{1}{5} \cdot \int 3 x^{2} d x

3 x^{2} = x^{\frac{2}{3}},

假定

x \geq 0

= - \frac{1}{5} \cdot \int x^{\frac{2}{3}} d x

使用幂法则

= - \frac{1}{5} \cdot \frac{3}{5} x^{\frac{5}{3}}

化简

- \frac{1}{5} \cdot \frac{3}{5} x^{\frac{5}{3}} : - \frac{3}{25} x^{\frac{5}{3}}

= - \frac{3}{25} x^{\frac{5}{3}}

解答补常数

= - \frac{3}{25} x^{\frac{5}{3}} + C

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