What is the integral of (sqrt(2-x))/(sqrt(x)) ?

The integral of (sqrt(2-x))/(sqrt(x)) is sqrt((2-x)/x)x+2arcsin(1/(sqrt(2))sqrt(x))+C

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

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

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

Solution steps

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

Apply Integration By Parts

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

= \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))

Simplify

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

Add a constant to the solution

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

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What is the integral of (sqrt(2-x))/(sqrt(x)) ?
The integral of (sqrt(2-x))/(sqrt(x)) is sqrt((2-x)/x)x+2arcsin(1/(sqrt(2))sqrt(x))+C