integral of (5-x)^2

解答

\int (5 - x)^{2} d x

25 x - 5 x^{2} + \frac{x ^{3}}{3} + C

求解步骤

\int (5 - x)^{2} d x

乘开

(5 - x)^{2} : 25 - 10 x + x^{2}

= \int 25 - 10 x + 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 25 d x - \int 10 x d x + \int x^{2} d x

\int 25 d x = 25 x

\int 10 x d x = 5 x^{2}

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

= 25 x - 5 x^{2} + \frac{x ^{3}}{3}

解答补常数

= 25 x - 5 x^{2} + \frac{x ^{3}}{3} + C

t an g e n t f (x) = x^{2} - 2 x - 4, at x = 2

\frac{\partial}{\partial t} (sin (x - a t))

l a pl a ce t r an s f or m cos (2 t) (1 + e^{- 3 t})

\frac{d}{d x} ((x^{3} + 1)^{5})

\frac{\partial}{\partial x} (e^{- \frac{1}{x}})