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受欢迎的微积分 >

integral of (3x+6)/((2x^2+8x+3)^2)

解答

\int \frac{3 x + 6}{( 2 x ^{2} + 8 x + 3 ) ^{2}} d x

解答

- \frac{3}{4 ( 2 x ^{2} + 8 x + 3 )} + C

求解步骤

\int \frac{3 x + 6}{( 2 x ^{2} + 8 x + 3 ) ^{2}} d x

使用换元积分法

= \int \frac{27 u}{( 2 u ^{2} - 45 ) ^{2}} d u

提出常数:

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

= 27 \cdot \int \frac{u}{( 2 u ^{2} - 45 ) ^{2}} d u

使用换元积分法

= 27 \cdot \int \frac{1}{4 v ^{2}} d v

提出常数:

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

= 27 \cdot \frac{1}{4} \cdot \int \frac{1}{v ^{2}} d v

使用幂法则

= 27 \cdot \frac{1}{4} (- \frac{1}{v})

代回

= 27 \cdot \frac{1}{4} (- \frac{1}{2 ( 3 x + 6 ) ^{2} - 45})

化简

27 \cdot \frac{1}{4} (- \frac{1}{2 ( 3 x + 6 ) ^{2} - 45}) : - \frac{3}{4 ( 2 x ^{2} + 8 x + 3 )}

= - \frac{3}{4 ( 2 x ^{2} + 8 x + 3 )}

解答补常数

= - \frac{3}{4 ( 2 x ^{2} + 8 x + 3 )} + C

作图

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