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受欢迎的微积分 >

integral of (6x^2)/(5sqrt(4x^3-3))

解答

\int \frac{6 x ^{2}}{5 4 x ^{3} - 3} d x

解答

\frac{1}{5} 4 x^{3} - 3 + C

求解步骤

\int \frac{6 x ^{2}}{5 4 x ^{3} - 3} d x

提出常数:

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

= \frac{6}{5} \cdot \int \frac{x ^{2}}{4 x ^{3} - 3} d x

使用换元积分法

= \frac{6}{5} \cdot \int \frac{1}{3 4 u - 3} d u

提出常数:

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

= \frac{6}{5} \cdot \frac{1}{3} \cdot \int \frac{1}{4 u - 3} d u

使用换元积分法

= \frac{6}{5} \cdot \frac{1}{3} \cdot \int \frac{1}{4 v} d v

提出常数:

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

= \frac{6}{5} \cdot \frac{1}{3} \cdot \frac{1}{4} \cdot \int \frac{1}{v} d v

使用幂法则

= \frac{6}{5} \cdot \frac{1}{3} \cdot \frac{1}{4} \cdot 2 v^{\frac{1}{2}}

代回

= \frac{6}{5} \cdot \frac{1}{3} \cdot \frac{1}{4} \cdot 2 (4 x^{3} - 3)^{\frac{1}{2}}

化简

\frac{6}{5} \cdot \frac{1}{3} \cdot \frac{1}{4} \cdot 2 (4 x^{3} - 3)^{\frac{1}{2}} : \frac{1}{5} 4 x^{3} - 3

= \frac{1}{5} 4 x^{3} - 3

解答补常数

= \frac{1}{5} 4 x^{3} - 3 + C

作图

流行的例子

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