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

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

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integral of sqrt(2/x)

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

\frac{2}{x} x + 2 x + C

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

= \frac{2}{x} x + 2 x

Add a constant to the solution

= \frac{2}{x} x + 2 x + C

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