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

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

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integral of 2/(sqrt(2x))

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

22 x + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \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

= 2 (\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

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

Simplify

2 (\frac{x}{2} - (- \frac{1}{2} x)) : 22 x

= 22 x

Add a constant to the solution

= 22 x + C

\frac{d}{d t} (2 cos (t) - 2)

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

\int y^{- 3} d y

\frac{\partial}{\partial y} (x y^{2} arctan (z))

(4 x + 2 y) d x + (2 x + 2 y) d y = 0

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