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

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

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integral of sqrt((x-1)/x)

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

\frac{x - 1}{x} x - ln x + x - 1 + C

Solution steps

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

Apply Integration By Parts

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

= \frac{x - 1}{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 = ln x + x - 1

= \frac{x - 1}{x} x - ln x + x - 1

Add a constant to the solution

= \frac{x - 1}{x} x - ln x + x - 1 + C

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