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受欢迎的微积分 >

integral of 3(3x+9)^7

解答

\int 3 (3 x + 9)^{7} d x

解答

\frac{1}{8} (3 x + 9)^{8} + C

求解步骤

\int 3 (3 x + 9)^{7} d x

提出常数:

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

= 3 \cdot \int (3 x + 9)^{7} d x

使用换元积分法

= 3 \cdot \int \frac{u ^{7}}{3} d u

提出常数:

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

= 3 \cdot \frac{1}{3} \cdot \int u^{7} d u

使用幂法则

= 3 \cdot \frac{1}{3} \cdot \frac{u ^{8}}{8}

u = 3 x + 9

代回

= 3 \cdot \frac{1}{3} \cdot \frac{( 3 x + 9 ) ^{8}}{8}

化简

3 \cdot \frac{1}{3} \cdot \frac{( 3 x + 9 ) ^{8}}{8} : \frac{1}{8} (3 x + 9)^{8}

= \frac{1}{8} (3 x + 9)^{8}

解答补常数

= \frac{1}{8} (3 x + 9)^{8} + C

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