integral from 0 to 2 of x/(x-2)

解答

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

发散

求解步骤

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

使用换元积分法

= \int_{- 2}^{0} \frac{u + 2}{u} d u

乘开

\frac{u + 2}{u} : 1 + \frac{2}{u}

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

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}^{0} 1 d u + \int_{- 2}^{0} \frac{2}{u} d u

\int_{- 2}^{0} 1 d u = 2

\int_{- 2}^{0} \frac{2}{u} d u =

发散

如果表达式有部分发散，则整个表达式发散

= 发散

\int_{1}^{e^{3}} \frac{4 ln ( x )}{x} d x

\int_{- 1}^{3} 3 x^{2} + 8 x d x

\int_{6}^{7} 3^{x} d x

\int_{1}^{\infty} arccot (x) d x

\int_{0}^{\frac{3 π}{2}} 7 sin (x) d x