integral of (-4x-10)/(x^3)

解答

\int \frac{- 4 x - 10}{x ^{3}} d x

\frac{2 x + 5}{x ^{2}} + \frac{2}{x} + C

求解步骤

\int \frac{- 4 x - 10}{x ^{3}} d x

使用分布积分法

= \frac{2 x + 5}{x ^{2}} - \int \frac{2}{x ^{2}} d x

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

= \frac{2 x + 5}{x ^{2}} - (- \frac{2}{x})

化简

= \frac{2 x + 5}{x ^{2}} + \frac{2}{x}

解答补常数

= \frac{2 x + 5}{x ^{2}} + \frac{2}{x} + C

a re a f (x) = x^{2} - 12, g (x) = x - 6, x = - 2, x = 3

\int 3 x^{7} + 4 x^{5} - 2 x^{3} - x + 1 d x

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

\frac{\partial}{\partial x} (z e^{x y})

\frac{d}{d x} (\frac{1400}{( 1 + 6 e ^{- 0.02 x} )})