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受欢迎的微积分 >

integral of 2sqrt(3x-1)

解答

\int 2 3 x - 1 d x

解答

\frac{4}{9} (3 x - 1)^{\frac{3}{2}} + C

求解步骤

\int 2 3 x - 1 d x

提出常数:

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

= 2 \cdot \int 3 x - 1 d x

使用换元积分法

= 2 \cdot \int \frac{u}{3} d u

提出常数:

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

= 2 \cdot \frac{1}{3} \cdot \int u d u

使用幂法则

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

u = 3 x - 1

代回

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

化简

2 \cdot \frac{1}{3} \cdot \frac{2}{3} (3 x - 1)^{\frac{3}{2}} : \frac{4}{9} (3 x - 1)^{\frac{3}{2}}

= \frac{4}{9} (3 x - 1)^{\frac{3}{2}}

解答补常数

= \frac{4}{9} (3 x - 1)^{\frac{3}{2}} + C

作图

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