integral of (9-x)sqrt(x)

解答

\int (9 - x) x d x

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

求解步骤

\int (9 - x) x d x

乘开

(9 - x) x : 9 x - x^{\frac{3}{2}}

= \int 9 x - x^{\frac{3}{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 9 x d x - \int x^{\frac{3}{2}} d x

\int 9 x d x = 6 x^{\frac{3}{2}}

\int x^{\frac{3}{2}} d x = \frac{2}{5} x^{\frac{5}{2}}

= 6 x^{\frac{3}{2}} - \frac{2}{5} x^{\frac{5}{2}}

解答补常数

= 6 x^{\frac{3}{2}} - \frac{2}{5} x^{\frac{5}{2}} + C

\frac{\partial}{\partial x} (x \cdot e^{(- y)})

t an g e n t \frac{x}{x - 2}

y^{^{''}} + 4 y^{^{'}} + 4 y = 3 e^{- 2 t}

x^{'} (t) = \frac{1}{3 x ^{2} + 1}, x (0) = 1

\frac{\partial}{\partial x} (e^{- 6 t} cos (π x))