What is the integral of sqrt(1/x-1) ?

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

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integral of sqrt(1/x-1)

\int \frac{1}{x} - 1 d x

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

Solution steps

\int \frac{1}{x} - 1 d x

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

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