integral of (x+1)/(sqrt(x^3))

解答

\int \frac{x + 1}{x ^{3}} d x

2 x - \frac{2}{x} + C

求解步骤

\int \frac{x + 1}{x ^{3}} d x

乘开

\frac{x + 1}{x ^{3}} : \frac{x}{x ^{3}} + \frac{1}{x ^{3}}

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{x}{x ^{3}} d x + \int \frac{1}{x ^{3}} d x

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

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

= 2 x - \frac{2}{x}

解答补常数

= 2 x - \frac{2}{x} + C

z \to i lim (z^{2} + 2 z)

y^{^{''}} - 4 y^{^{'}} + 4 y = \frac{e ^{2 x}}{x}

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

\frac{d}{d s} (\frac{s}{s ^{2} + 25})

\int (4 x + 3)^{7} d x