integral of 1/(x^5)-3/(x^2)

解答

\int \frac{1}{x ^{5}} - \frac{3}{x ^{2}} d x

- \frac{1}{4 x ^{4}} + \frac{3}{x} + C

求解步骤

\int \frac{1}{x ^{5}} - \frac{3}{x ^{2}} 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 ^{5}} d x - \int \frac{3}{x ^{2}} d x

\int \frac{1}{x ^{5}} d x = - \frac{1}{4 x ^{4}}

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

= - \frac{1}{4 x ^{4}} - (- \frac{3}{x})

化简

= - \frac{1}{4 x ^{4}} + \frac{3}{x}

解答补常数

= - \frac{1}{4 x ^{4}} + \frac{3}{x} + C

x y^{^{'}} + 2 y = x^{2} - x + 1

t an g e n t f (x) = ln (x^{2} - 9 x + 1), (9, 0)

s l o p e (- 2, 2), (1, - 2)

l a pl a ce t r an s f or m 6 t^{2}

\int \frac{1}{484 - x ^{2}} d x