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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

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