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

\int x^{2} sec^{2} (x) d x

\int (x + 7)^{2} d x

\int \frac{x ^{2}}{2 + x ^{3}} d x

x, \frac{x ^{2}}{4}, 0, 2

2 y^{^{'''}} + 3 y^{^{''}} - 11 y^{^{'}} - 6 y = 0

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