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

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

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

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

\frac{1}{2} x - 2 x + C

Solution steps

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

Expand

\frac{x - 2}{2 x} : \frac{1}{2} - \frac{1}{x}

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

= \frac{1}{2} x - 2 x

Add a constant to the solution

= \frac{1}{2} x - 2 x + C

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