integral from 2 to 4 of 1/((x-4)(x-1))

解答

\int_{2}^{4} \frac{1}{( x - 4 ) ( x - 1 )} d x

发散

求解步骤

\int_{2}^{4} \frac{1}{( x - 4 ) ( x - 1 )} d x

将

\frac{1}{( x - 4 ) ( x - 1 )}

用部份分式展开:

\frac{1}{3 ( x - 4 )} - \frac{1}{3 ( x - 1 )}

= \int_{2}^{4} \frac{1}{3 ( x - 4 )} - \frac{1}{3 ( x - 1 )} d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{2}^{4} \frac{1}{3 ( x - 4 )} d x - \int_{2}^{4} \frac{1}{3 ( x - 1 )} d x

\int_{2}^{4} \frac{1}{3 ( x - 4 )} d x =

发散

如果表达式有部分发散，则整个表达式发散

= 发散

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