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受欢迎的微积分 >

integral of (3y)/(sqrt(2y^2+5))

解答

\int \frac{3 y}{2 y ^{2} + 5} d y

解答

\frac{3}{2} 2 y^{2} + 5 + C

求解步骤

\int \frac{3 y}{2 y ^{2} + 5} d y

提出常数:

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

= 3 \cdot \int \frac{y}{2 y ^{2} + 5} d y

使用换元积分法

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

提出常数:

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

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

使用幂法则

= 3 \cdot \frac{1}{4} \cdot 2 u^{\frac{1}{2}}

u = 2 y^{2} + 5

代回

= 3 \cdot \frac{1}{4} \cdot 2 (2 y^{2} + 5)^{\frac{1}{2}}

化简

3 \cdot \frac{1}{4} \cdot 2 (2 y^{2} + 5)^{\frac{1}{2}} : \frac{3}{2} 2 y^{2} + 5

= \frac{3}{2} 2 y^{2} + 5

解答补常数

= \frac{3}{2} 2 y^{2} + 5 + C

作图

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