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

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

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integral of 1/(sqrt(2ax))

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

\frac{2 x}{a} + C

Solution steps

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

2 a x = 2 a x

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

Take the constant out:

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

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

\frac{1}{a x} = \frac{1}{a} \frac{1}{x}

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

Take the constant out:

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

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

Apply the Power Rule

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

= \frac{1}{2} \cdot \frac{1}{a} \cdot 2 x^{\frac{1}{2}}

Simplify

\frac{1}{2} \cdot \frac{1}{a} \cdot 2 x^{\frac{1}{2}} : \frac{2 x}{a}

= \frac{2 x}{a}

Add a constant to the solution

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

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