integral of (sqrt(x)+sqrt(2))/(sqrt(2x))

解答

\int \frac{x + 2}{2 x} d x

\frac{1}{2} x + 2 x + C

求解步骤

\int \frac{x + 2}{2 x} d x

乘开

\frac{x + 2}{2 x} : \frac{1}{2} + \frac{1}{x}

= \int \frac{1}{2} + \frac{1}{x} 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}{2} d x + \int \frac{1}{x} d x

\int \frac{1}{2} d x = \frac{1}{2} x

\int \frac{1}{x} d x = 2 x

= \frac{1}{2} x + 2 x

解答补常数

= \frac{1}{2} x + 2 x + C