What is the integral of 1/(xsqrt(3x)) ?

The integral of 1/(xsqrt(3x)) is -2/(sqrt(3)\sqrt{x)}+C

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integral of 1/(xsqrt(3x))

\int \frac{1}{x 3 x} d x

- \frac{2}{3 x} + C

Solution steps

\int \frac{1}{x 3 x} d x

3 x = 3 x

= \int \frac{1}{3 x x} d x

Take the constant out:

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

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

Simplify

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

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

Apply the Power Rule

: - \frac{2}{x}

= \frac{1}{3} (- \frac{2}{x})

Simplify

\frac{1}{3} (- \frac{2}{x}) : - \frac{2}{3 x}

= - \frac{2}{3 x}

Add a constant to the solution

= - \frac{2}{3 x} + C

\frac{d}{d x} (2 ln (x^{2} + y^{2}))

t y^{^{'}} = (1 - y^{2})^{\frac{1}{2}}

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

\frac{1}{x - 1}, 18

sin (x), cos (x)

What is the integral of 1/(xsqrt(3x)) ?
The integral of 1/(xsqrt(3x)) is -2/(sqrt(3)\sqrt{x)}+C