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受欢迎的微积分 >

integral of (7x^2)/(sqrt(4x^3-5))

解答

\int \frac{7 x ^{2}}{4 x ^{3} - 5} d x

解答

\frac{7}{6} 4 x^{3} - 5 + C

求解步骤

\int \frac{7 x ^{2}}{4 x ^{3} - 5} d x

提出常数:

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

= 7 \cdot \int \frac{x ^{2}}{4 x ^{3} - 5} d x

使用换元积分法

= 7 \cdot \int \frac{1}{12 u} d u

提出常数:

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

= 7 \cdot \frac{1}{12} \cdot \int \frac{1}{u} d u

使用幂法则

= 7 \cdot \frac{1}{12} \cdot 2 u^{\frac{1}{2}}

u = 4 x^{3} - 5

代回

= 7 \cdot \frac{1}{12} \cdot 2 (4 x^{3} - 5)^{\frac{1}{2}}

化简

7 \cdot \frac{1}{12} \cdot 2 (4 x^{3} - 5)^{\frac{1}{2}} : \frac{7}{6} 4 x^{3} - 5

= \frac{7}{6} 4 x^{3} - 5

解答补常数

= \frac{7}{6} 4 x^{3} - 5 + C

作图

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