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受欢迎的微积分 >

integral of (4x+3)^9

解答

\int (4 x + 3)^{9} d x

解答

\frac{1}{40} (4 x + 3)^{10} + C

求解步骤

\int (4 x + 3)^{9} d x

使用换元积分法

= \int \frac{u ^{9}}{4} d u

提出常数:

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

= \frac{1}{4} \cdot \int u^{9} d u

使用幂法则

= \frac{1}{4} \cdot \frac{u ^{10}}{10}

u = 4 x + 3

代回

= \frac{1}{4} \cdot \frac{( 4 x + 3 ) ^{10}}{10}

化简

\frac{1}{4} \cdot \frac{( 4 x + 3 ) ^{10}}{10} : \frac{1}{40} (4 x + 3)^{10}

= \frac{1}{40} (4 x + 3)^{10}

解答补常数

= \frac{1}{40} (4 x + 3)^{10} + C

作图

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