integral of ((x-4)/(x^9))

解答

\int (\frac{x - 4}{x ^{9}}) d x

- \frac{1}{7 x ^{7}} + \frac{1}{2 x ^{8}} + C

求解步骤

\int \frac{x - 4}{x ^{9}} d x

乘开

\frac{x - 4}{x ^{9}} : \frac{1}{x ^{8}} - \frac{4}{x ^{9}}

= \int \frac{1}{x ^{8}} - \frac{4}{x ^{9}} 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 \frac{1}{x ^{8}} d x - \int \frac{4}{x ^{9}} d x

\int \frac{1}{x ^{8}} d x = - \frac{1}{7 x ^{7}}

\int \frac{4}{x ^{9}} d x = - \frac{1}{2 x ^{8}}

= - \frac{1}{7 x ^{7}} - (- \frac{1}{2 x ^{8}})

化简

= - \frac{1}{7 x ^{7}} + \frac{1}{2 x ^{8}}

解答补常数

= - \frac{1}{7 x ^{7}} + \frac{1}{2 x ^{8}} + C

a re a y = (x - 2)^{2}, y = 4 - x, y = 2 x - 2

\frac{d}{d x} (\frac{75}{12 + x ^{2} + y ^{2}})

x \to 3 lim (x 18 - x^{2})

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

d er i v a t i v e y = 2 e^{x} cos (x)