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

The integral of (a^{2/3}-x^{2/3}) is a^{2/3}x-3/5 x^{5/3}+C

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

\int (a^{\frac{2}{3}} - x^{\frac{2}{3}}) d x

a^{\frac{2}{3}} x - \frac{3}{5} x^{\frac{5}{3}} + C

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int a^{\frac{2}{3}} d x - \int x^{\frac{2}{3}} d x

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

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

= a^{\frac{2}{3}} x - \frac{3}{5} x^{\frac{5}{3}}

Add a constant to the solution

= a^{\frac{2}{3}} x - \frac{3}{5} x^{\frac{5}{3}} + C

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What is the integral of (a^{2/3}-x^{2/3}) ?
The integral of (a^{2/3}-x^{2/3}) is a^{2/3}x-3/5 x^{5/3}+C