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受欢迎的微积分 >

integral of (2x)^2(5+3^4)^{1/4}

解答

\int (2 x)^{2} (5 + 3^{4})^{\frac{1}{4}} d x

解答

\frac{4 \cdot 8 6 ^{\frac{1}{4}} x ^{3}}{3} + C

求解步骤

\int (2 x)^{2} (5 + 3^{4})^{\frac{1}{4}} d x

提出常数:

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

= (5 + 3^{4})^{\frac{1}{4}} \cdot \int (2 x)^{2} d x

化简

= 8 6^{\frac{1}{4}} \cdot \int (2 x)^{2} d x

化简

(2 x)^{2} : 4 x^{2}

= 8 6^{\frac{1}{4}} \cdot \int 4 x^{2} d x

提出常数:

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

= 8 6^{\frac{1}{4}} \cdot 4 \cdot \int x^{2} d x

使用幂法则

= 8 6^{\frac{1}{4}} \cdot 4 \cdot \frac{x ^{3}}{3}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{4 \cdot 8 6 ^{\frac{1}{4}} x ^{3}}{3}

解答补常数

= \frac{4 \cdot 8 6 ^{\frac{1}{4}} x ^{3}}{3} + C

作图

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