What is the integral of (2x^{3/2})/(3x) ?

The integral of (2x^{3/2})/(3x) is 4/9 x^{3/2}+C

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integral of (2x^{3/2})/(3x)

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

\frac{4}{9} x^{\frac{3}{2}} + C

Solution steps

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

Simplify

\frac{x ^{\frac{3}{2}}}{x} : x^{\frac{1}{2}}

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

Apply the Power Rule

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

= \frac{2}{3} \cdot \frac{2}{3} x^{\frac{3}{2}}

Simplify

\frac{2}{3} \cdot \frac{2}{3} x^{\frac{3}{2}} : \frac{4}{9} x^{\frac{3}{2}}

= \frac{4}{9} x^{\frac{3}{2}}

Add a constant to the solution

= \frac{4}{9} x^{\frac{3}{2}} + C

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x + 2

x - 2

What is the integral of (2x^{3/2})/(3x) ?
The integral of (2x^{3/2})/(3x) is 4/9 x^{3/2}+C