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

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

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integral of 1/(xsqrt(2x))

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

- \frac{2}{x} + C

Solution steps

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

2 x = 2 x

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

Simplify

x x : x^{\frac{3}{2}}

= \frac{1}{2} \cdot \int \frac{1}{x ^{\frac{3}{2}}} d x

Apply the Power Rule

: - \frac{2}{x}

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

Simplify

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

= - \frac{2}{x}

Add a constant to the solution

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

\frac{d y}{d x} = \frac{8 x 4 - y ^{2}}{4 - y ^{2}}

\int \frac{1}{( 1 + sin ( x ) )} d x

x^{2} - 4, - 2 x - 3, - 1, 0

\int (3 x - 2) \cdot e^{- x} d x

x \to 5 + lim (5 - x)

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