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受欢迎的微积分 >

integral of (6x)/((3x^2-7)^{12)}

解答

\int \frac{6 x}{( 3 x ^{2} - 7 ) ^{12}} d x

解答

- \frac{1}{11 ( 3 x ^{2} - 7 ) ^{11}} + C

求解步骤

\int \frac{6 x}{( 3 x ^{2} - 7 ) ^{12}} d x

提出常数:

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

= 6 \cdot \int \frac{x}{( 3 x ^{2} - 7 ) ^{12}} d x

使用换元积分法

= 6 \cdot \int \frac{1}{6 u ^{12}} d u

提出常数:

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

= 6 \cdot \frac{1}{6} \cdot \int \frac{1}{u ^{12}} d u

使用幂法则

= 6 \cdot \frac{1}{6} (- \frac{1}{11 u ^{11}})

u = 3 x^{2} - 7

代回

= 6 \cdot \frac{1}{6} (- \frac{1}{11 ( 3 x ^{2} - 7 ) ^{11}})

化简

6 \cdot \frac{1}{6} (- \frac{1}{11 ( 3 x ^{2} - 7 ) ^{11}}) : - \frac{1}{11 ( 3 x ^{2} - 7 ) ^{11}}

= - \frac{1}{11 ( 3 x ^{2} - 7 ) ^{11}}

解答补常数

= - \frac{1}{11 ( 3 x ^{2} - 7 ) ^{11}} + C

作图

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