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受欢迎的微积分 >

integral of (3x)/((2-5x^2)^2)

解答

\int \frac{3 x}{( 2 - 5 x ^{2} ) ^{2}} d x

解答

\frac{3}{10 ( 2 - 5 x ^{2} )} + C

求解步骤

\int \frac{3 x}{( 2 - 5 x ^{2} ) ^{2}} d x

提出常数:

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

= 3 \cdot \int \frac{x}{( 2 - 5 x ^{2} ) ^{2}} d x

使用换元积分法

= 3 \cdot \int \frac{1}{2 ( 2 - 5 u ) ^{2}} d u

提出常数:

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

= 3 \cdot \frac{1}{2} \cdot \int \frac{1}{( 2 - 5 u ) ^{2}} d u

使用换元积分法

= 3 \cdot \frac{1}{2} \cdot \int - \frac{1}{5 v ^{2}} d v

提出常数:

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

= 3 \cdot \frac{1}{2} (- \frac{1}{5} \cdot \int \frac{1}{v ^{2}} d v)

使用幂法则

= 3 \cdot \frac{1}{2} (- \frac{1}{5} (- \frac{1}{v}))

代回

= 3 \cdot \frac{1}{2} (- \frac{1}{5} (- \frac{1}{2 - 5 x ^{2}}))

化简

3 \cdot \frac{1}{2} (- \frac{1}{5} (- \frac{1}{2 - 5 x ^{2}})) : \frac{3}{10 ( 2 - 5 x ^{2} )}

= \frac{3}{10 ( 2 - 5 x ^{2} )}

解答补常数

= \frac{3}{10 ( 2 - 5 x ^{2} )} + C

作图

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