integral of 6/((x-2)^2)

解答

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

- \frac{6}{x - 2} + C

求解步骤

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

提出常数:

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

= 6 \cdot \int \frac{1}{( x - 2 ) ^{2}} d x

使用换元积分法

= 6 \cdot \int \frac{1}{u ^{2}} d u

使用幂法则

= 6 (- \frac{1}{u})

u = x - 2

代回

= 6 (- \frac{1}{x - 2})

化简

6 (- \frac{1}{x - 2}) : - \frac{6}{x - 2}

= - \frac{6}{x - 2}

解答补常数

= - \frac{6}{x - 2} + C

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