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受欢迎的微积分 >

integral of (2x^4)/(sqrt(1-8x^5))

解答

\int \frac{2 x ^{4}}{1 - 8 x ^{5}} d x

解答

- \frac{1}{10} 1 - 8 x^{5} + C

求解步骤

\int \frac{2 x ^{4}}{1 - 8 x ^{5}} d x

提出常数:

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

= 2 \cdot \int \frac{x ^{4}}{1 - 8 x ^{5}} d x

使用换元积分法

= 2 \cdot \int - \frac{1}{40 u} d u

提出常数:

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

= 2 (- \frac{1}{40} \cdot \int \frac{1}{u} d u)

使用幂法则

= 2 (- \frac{1}{40} \cdot 2 u^{\frac{1}{2}})

u = 1 - 8 x^{5}

代回

= 2 (- \frac{1}{40} \cdot 2 (1 - 8 x^{5})^{\frac{1}{2}})

化简

2 (- \frac{1}{40} \cdot 2 (1 - 8 x^{5})^{\frac{1}{2}}) : - \frac{1}{10} 1 - 8 x^{5}

= - \frac{1}{10} 1 - 8 x^{5}

解答补常数

= - \frac{1}{10} 1 - 8 x^{5} + C

作图

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