What is the integral of (1/(sqrt(2x))) ?

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

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integral of (1/(sqrt(2x)))

\int (\frac{1}{2 x}) d x

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

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