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

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

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integral of 2x^{2/3}

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

: \frac{3}{5} x^{\frac{5}{3}}

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

Simplify

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

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

Add a constant to the solution

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

t^{2} y^{^{'}} + t y = t^{5}

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