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受欢迎的微积分 >

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

解答

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

解答

- \frac{3}{16} (2 x^{2} + 4)^{\frac{4}{3}} + C

求解步骤

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

提出常数:

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

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

使用换元积分法

= - \int \frac{3 u}{4} d u

提出常数:

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

= - \frac{1}{4} \cdot \int 3 u d u

使用幂法则

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

u = 2 x^{2} + 4

代回

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

化简

- \frac{1}{4} \cdot \frac{3}{4} (2 x^{2} + 4)^{\frac{4}{3}} : - \frac{3}{16} (2 x^{2} + 4)^{\frac{4}{3}}

= - \frac{3}{16} (2 x^{2} + 4)^{\frac{4}{3}}

解答补常数

= - \frac{3}{16} (2 x^{2} + 4)^{\frac{4}{3}} + C

作图

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