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受欢迎的微积分 >

integral from 1 to 3 of (x+2)(x-1)^5

解答

\int_{1}^{3} (x + 2) (x - 1)^{5} d x

解答

\frac{352}{7}

+1

十进制

50.28571 \dots

求解步骤

\int_{1}^{3} (x + 2) (x - 1)^{5} d x

乘以

x + 2

的共轭根式

: \frac{x ^{2} - 4}{x - 2}

= \int_{1}^{3} \frac{x ^{2} - 4}{x - 2} (x - 1)^{5} d x

找到无定义的点（奇点）:

x = 2

如果存在

b, a < b < c, f (b) =

无定义

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{1}^{2} \frac{x ^{2} - 4}{x - 2} (x - 1)^{5} d x + \int_{2}^{3} \frac{x ^{2} - 4}{x - 2} (x - 1)^{5} d x

\int_{1}^{2} \frac{x ^{2} - 4}{x - 2} (x - 1)^{5} d x = \frac{9}{14}

\int_{2}^{3} \frac{x ^{2} - 4}{x - 2} (x - 1)^{5} d x = \frac{695}{14}

= \frac{9}{14} + \frac{695}{14}

化简

\frac{9}{14} + \frac{695}{14} : \frac{352}{7}

= \frac{352}{7}

作图

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