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

解答

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

\frac{2 - x}{x} x + 2 arcsin (\frac{1}{2} x) + C

求解步骤

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

使用分布积分法

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

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

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

化简

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

解答补常数

= \frac{2 - x}{x} x + 2 arcsin (\frac{1}{2} x) + C

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