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受欢迎的微积分 >

integral of (4x^5)/(sqrt(5-12x^6))

解答

\int \frac{4 x ^{5}}{5 - 12 x ^{6}} d x

解答

- \frac{1}{9} 5 - 12 x^{6} + C

求解步骤

\int \frac{4 x ^{5}}{5 - 12 x ^{6}} d x

提出常数:

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

= 4 \cdot \int \frac{x ^{5}}{5 - 12 x ^{6}} d x

使用换元积分法

= 4 \cdot \int - \frac{1}{72 u} d u

提出常数:

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

= 4 (- \frac{1}{72} \cdot \int \frac{1}{u} d u)

使用幂法则

= 4 (- \frac{1}{72} \cdot 2 u^{\frac{1}{2}})

u = 5 - 12 x^{6}

代回

= 4 (- \frac{1}{72} \cdot 2 (5 - 12 x^{6})^{\frac{1}{2}})

化简

4 (- \frac{1}{72} \cdot 2 (5 - 12 x^{6})^{\frac{1}{2}}) : - \frac{1}{9} 5 - 12 x^{6}

= - \frac{1}{9} 5 - 12 x^{6}

解答补常数

= - \frac{1}{9} 5 - 12 x^{6} + C

作图

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