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受欢迎的微积分 >

integral of (-13300)/((5x+40)^2)

解答

\int \frac{- 13300}{( 5 x + 40 ) ^{2}} d x

解答

\frac{532}{x + 8} + C

求解步骤

\int \frac{- 13300}{( 5 x + 40 ) ^{2}} d x

提出常数:

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

= - 13300 \cdot \int \frac{1}{( 5 x + 40 ) ^{2}} d x

使用换元积分法

= - 13300 \cdot \int \frac{1}{5 u ^{2}} d u

提出常数:

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

= - 13300 \cdot \frac{1}{5} \cdot \int \frac{1}{u ^{2}} d u

使用幂法则

= - 13300 \cdot \frac{1}{5} (- \frac{1}{u})

u = 5 x + 40

代回

= - 13300 \cdot \frac{1}{5} (- \frac{1}{5 x + 40})

化简

- 13300 \cdot \frac{1}{5} (- \frac{1}{5 x + 40}) : \frac{532}{x + 8}

= \frac{532}{x + 8}

解答补常数

= \frac{532}{x + 8} + C

作图

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