What is the integral of 10x^{2/3} ?

The integral of 10x^{2/3} is 6x^{5/3}+C

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integral of 10x^{2/3}

\int 10 x^{\frac{2}{3}} d x

6 x^{\frac{5}{3}} + C

Solution steps

\int 10 x^{\frac{2}{3}} d x

Take the constant out:

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

= 10 \cdot \int x^{\frac{2}{3}} d x

Apply the Power Rule

= 10 \cdot \frac{3}{5} x^{\frac{5}{3}}

Simplify

10 \cdot \frac{3}{5} x^{\frac{5}{3}} : 6 x^{\frac{5}{3}}

= 6 x^{\frac{5}{3}}

Add a constant to the solution

= 6 x^{\frac{5}{3}} + C