What is the integral of 1/3 x^{3/2} ?

The integral of 1/3 x^{3/2} is 2/15 x^{5/2}+C

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integral of 1/3 x^{3/2}

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

\frac{2}{15} x^{\frac{5}{2}} + C

Solution steps

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

Apply the Power Rule

: \frac{2}{5} x^{\frac{5}{2}}

= \frac{1}{3} \cdot \frac{2}{5} x^{\frac{5}{2}}

Simplify

\frac{1}{3} \cdot \frac{2}{5} x^{\frac{5}{2}} : \frac{2}{15} x^{\frac{5}{2}}

= \frac{2}{15} x^{\frac{5}{2}}

Add a constant to the solution

= \frac{2}{15} x^{\frac{5}{2}} + C

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What is the integral of 1/3 x^{3/2} ?
The integral of 1/3 x^{3/2} is 2/15 x^{5/2}+C