integral of (3/(x^2)-2/(x^3))

解答

\int (\frac{3}{x ^{2}} - \frac{2}{x ^{3}}) d x

- \frac{3}{x} + \frac{1}{x ^{2}} + C

求解步骤

\int \frac{3}{x ^{2}} - \frac{2}{x ^{3}} 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{3}{x ^{2}} d x - \int \frac{2}{x ^{3}} d x

\int \frac{3}{x ^{2}} d x = - \frac{3}{x}

\int \frac{2}{x ^{3}} d x = - \frac{1}{x ^{2}}

= - \frac{3}{x} - (- \frac{1}{x ^{2}})

化简

= - \frac{3}{x} + \frac{1}{x ^{2}}

解答补常数

= - \frac{3}{x} + \frac{1}{x ^{2}} + C

n = 1 \sum \infty \frac{n !}{n \cdot 3 ^{n}}

a re a y = 18 sin (x), y = 18 cos (x)

a re a x^{2} - 4 x + 3, - x^{2} + 2 x + 3, 4, 0

t^{2} \frac{d y}{d t} - t = 1 + y + t y, y (1) = 8

d er i v a t i v e y = \frac{ln ( 6 x )}{6 x}