What is the integral of 2/5 x^{5/3} ?

The integral of 2/5 x^{5/3} is 3/20 x^{8/3}+C

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integral of 2/5 x^{5/3}

\int \frac{2}{5} x^{\frac{5}{3}} d x

\frac{3}{20} x^{\frac{8}{3}} + C

Solution steps

\int \frac{2}{5} x^{\frac{5}{3}} d x

Take the constant out:

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

= \frac{2}{5} \cdot \int x^{\frac{5}{3}} d x

Apply the Power Rule

: \frac{3}{8} x^{\frac{8}{3}}

= \frac{2}{5} \cdot \frac{3}{8} x^{\frac{8}{3}}

Simplify

\frac{2}{5} \cdot \frac{3}{8} x^{\frac{8}{3}} : \frac{3}{20} x^{\frac{8}{3}}

= \frac{3}{20} x^{\frac{8}{3}}

Add a constant to the solution

= \frac{3}{20} x^{\frac{8}{3}} + C

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What is the integral of 2/5 x^{5/3} ?
The integral of 2/5 x^{5/3} is 3/20 x^{8/3}+C