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受欢迎的微积分 >

integral of 2x^2\sqrt[3]{3x^3+4}

解答

\int 2 x^{2} 3 3 x^{3} + 4 d x

解答

\frac{1}{6} (3 x^{3} + 4)^{\frac{4}{3}} + C

求解步骤

\int 2 x^{2} 3 3 x^{3} + 4 d x

提出常数:

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

= 2 \cdot \int x^{2} 3 3 x^{3} + 4 d x

使用换元积分法

= 2 \cdot \int \frac{3 3 u + 4}{3} d u

提出常数:

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

= 2 \cdot \frac{1}{3} \cdot \int 3 3 u + 4 d u

使用换元积分法

= 2 \cdot \frac{1}{3} \cdot \int \frac{3 v}{3} d v

提出常数:

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

= 2 \cdot \frac{1}{3} \cdot \frac{1}{3} \cdot \int 3 v d v

使用幂法则

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

代回

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

化简

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

= \frac{1}{6} (3 x^{3} + 4)^{\frac{4}{3}}

解答补常数

= \frac{1}{6} (3 x^{3} + 4)^{\frac{4}{3}} + C

作图

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