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受欢迎的微积分 >

integral of sqrt(8-3x)

解答

\int 8 - 3 x d x

解答

- \frac{2}{9} (8 - 3 x)^{\frac{3}{2}} + C

求解步骤

\int 8 - 3 x d x

使用换元积分法

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

提出常数:

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

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

使用幂法则

= - \frac{1}{3} \cdot \frac{2}{3} u^{\frac{3}{2}}

u = 8 - 3 x

代回

= - \frac{1}{3} \cdot \frac{2}{3} (8 - 3 x)^{\frac{3}{2}}

化简

- \frac{1}{3} \cdot \frac{2}{3} (8 - 3 x)^{\frac{3}{2}} : - \frac{2}{9} (8 - 3 x)^{\frac{3}{2}}

= - \frac{2}{9} (8 - 3 x)^{\frac{3}{2}}

解答补常数

= - \frac{2}{9} (8 - 3 x)^{\frac{3}{2}} + C

作图

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