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受欢迎的微积分 >

integral of 2/((sqrt(3x+2)))

解答

\int \frac{2}{( 3 x + 2 )} d x

解答

\frac{4}{3} 3 x + 2 + C

求解步骤

\int \frac{2}{3 x + 2} d x

提出常数:

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

= 2 \cdot \int \frac{1}{3 x + 2} d x

使用换元积分法

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

使用幂法则

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

u = 3 x + 2

代回

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

化简

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

= \frac{4}{3} 3 x + 2

解答补常数

= \frac{4}{3} 3 x + 2 + C

作图

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