integral from 0 to 2 of (4x+3)/(x^4)

解答

\int_{0}^{2} \frac{4 x + 3}{x ^{4}} d x

发散

求解步骤

\int_{0}^{2} \frac{4 x + 3}{x ^{4}} d x

乘开

\frac{4 x + 3}{x ^{4}} : \frac{4}{x ^{3}} + \frac{3}{x ^{4}}

= \int_{0}^{2} \frac{4}{x ^{3}} + \frac{3}{x ^{4}} 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_{0}^{2} \frac{4}{x ^{3}} d x + \int_{0}^{2} \frac{3}{x ^{4}} d x

\int_{0}^{2} \frac{4}{x ^{3}} d x =

发散

如果表达式有部分发散，则整个表达式发散

= 发散

\int (5 x^{3} - 7 x^{2} + 2 x + 1) d x

\frac{d}{d x} (30 + \frac{1}{x + 1} - 3 x^{2})

\frac{d}{d x} (\frac{1}{5 x ^{2} + 2 x})

in v erse l a pl a ce \frac{5 s + 3}{( s - 1 ) ( s ^{2} + 2 s + 5 )}

\frac{\partial}{\partial y} (x^{2} + e^{x y})