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受欢迎的微积分 >

integral of \sqrt[3]{4-3x^2}(-6x)

解答

\int 3 4 - 3 x^{2} (- 6 x) d x

解答

\frac{3}{4} (4 - 3 x^{2})^{\frac{4}{3}} + C

求解步骤

\int 3 4 - 3 x^{2} (- 6 x) d x

化简

= \int - 6 x 3 4 - 3 x^{2} d x

提出常数:

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

= - 6 \cdot \int x 3 4 - 3 x^{2} d x

使用换元积分法

= - 6 \cdot \int - \frac{3 u}{6} d u

提出常数:

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

= - 6 (- \frac{1}{6} \cdot \int 3 u d u)

使用幂法则

= - 6 (- \frac{1}{6} \cdot \frac{3}{4} u^{\frac{4}{3}})

u = 4 - 3 x^{2}

代回

= - 6 (- \frac{1}{6} \cdot \frac{3}{4} (4 - 3 x^{2})^{\frac{4}{3}})

化简

- 6 (- \frac{1}{6} \cdot \frac{3}{4} (4 - 3 x^{2})^{\frac{4}{3}}) : \frac{3}{4} (4 - 3 x^{2})^{\frac{4}{3}}

= \frac{3}{4} (4 - 3 x^{2})^{\frac{4}{3}}

解答补常数

= \frac{3}{4} (4 - 3 x^{2})^{\frac{4}{3}} + C

作图

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