integral of 2/(sqrt(2x))

解答

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

22 x + C

求解步骤

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

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

使用分布积分法

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

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

= 2 (\frac{x}{2} - (- \frac{1}{2} x))

化简

2 (\frac{x}{2} - (- \frac{1}{2} x)) : 22 x

= 22 x

解答补常数

= 22 x + C