What is the integral of 2/(3xsqrt(x)) ?

The integral of 2/(3xsqrt(x)) is -4/(3sqrt(x))+C

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integral of 2/(3xsqrt(x))

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

- \frac{4}{3 x} + C

Solution steps

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

Take the constant out:

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

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

Simplify

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

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

Apply the Power Rule

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

Simplify

\frac{2}{3} (- \frac{2}{x}) : - \frac{4}{3 x}

= - \frac{4}{3 x}

Add a constant to the solution

= - \frac{4}{3 x} + C

What is the integral of 2/(3xsqrt(x)) ?
The integral of 2/(3xsqrt(x)) is -4/(3sqrt(x))+C