integral from 0 to 4 of x/(x^2-1)

解答

\int_{0}^{4} \frac{x}{x ^{2} - 1} d x

发散

求解步骤

\int_{0}^{4} \frac{x}{x ^{2} - 1} d x

找到无定义的点（奇点）:

x = 1

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_{0}^{1} \frac{x}{x ^{2} - 1} d x + \int_{1}^{4} \frac{x}{x ^{2} - 1} d x

\int_{0}^{1} \frac{x}{x ^{2} - 1} d x =

发散

如果表达式有部分发散，则整个表达式发散

= 发散

\frac{\partial}{\partial x} (3 x + 2 y - 3)

a re a y = x^{2}, y = 3 - x, (0, 1.3)

d er i v a t i v e f (x) = 3 x^{2} e^{x} + e^{x} (x^{3} + 1)

y^{^{'}} = 18.2 - 0.7 y

x \to 4 lim (x)