What is the integral of sqrt((x-6)/x) ?

The integral of sqrt((x-6)/x) is sqrt((x-6)/x)x-6ln| 1/(sqrt(6))sqrt(x-6)+sqrt(x/6)|+C

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integral of sqrt((x-6)/x)

\int \frac{x - 6}{x} d x

\frac{x - 6}{x} x - 6 ln \frac{1}{6} x - 6 + \frac{x}{6} + C

Solution steps

\int \frac{x - 6}{x} d x

Apply Integration By Parts

= \frac{x - 6}{x} x - \int \frac{3}{x ^{\frac{1}{2}} x - 6} d x

\int \frac{3}{x ^{\frac{1}{2}} x - 6} d x = 6 ln \frac{1}{6} x - 6 + \frac{x}{6}

= \frac{x - 6}{x} x - 6 ln \frac{1}{6} x - 6 + \frac{x}{6}

Add a constant to the solution

= \frac{x - 6}{x} x - 6 ln \frac{1}{6} x - 6 + \frac{x}{6} + C

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What is the integral of sqrt((x-6)/x) ?
The integral of sqrt((x-6)/x) is sqrt((x-6)/x)x-6ln| 1/(sqrt(6))sqrt(x-6)+sqrt(x/6)|+C