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受欢迎的微积分 >

integral of ((x-1))/((x^2-2x-35)^7)

解答

\int \frac{( x - 1 )}{( x ^{2} - 2 x - 35 ) ^{7}} d x

解答

- \frac{1}{12 ( x ^{2} - 2 x - 35 ) ^{6}} + C

求解步骤

\int \frac{x - 1}{( x ^{2} - 2 x - 35 ) ^{7}} d x

使用换元积分法

= \int \frac{u}{( u ^{2} - 36 ) ^{7}} d u

使用换元积分法

= \int \frac{1}{2 ( v - 36 ) ^{7}} d v

提出常数:

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

= \frac{1}{2} \cdot \int \frac{1}{( v - 36 ) ^{7}} d v

使用换元积分法

= \frac{1}{2} \cdot \int \frac{1}{w ^{7}} d w

使用幂法则

= \frac{1}{2} (- \frac{1}{6 w ^{6}})

代回

= \frac{1}{2} - \frac{1}{6 ( ( x - 1 ) ^{2} - 36 ) ^{6}}

化简

\frac{1}{2} - \frac{1}{6 ( ( x - 1 ) ^{2} - 36 ) ^{6}} : - \frac{1}{12 ( x ^{2} - 2 x - 35 ) ^{6}}

= - \frac{1}{12 ( x ^{2} - 2 x - 35 ) ^{6}}

解答补常数

= - \frac{1}{12 ( x ^{2} - 2 x - 35 ) ^{6}} + C

作图

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