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

x \to 0 lim (- 0. 5^{2} + 1)

x \to 3 lim (- 3 x^{2})

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

\int (3 x^{2} - 5 x^{\frac{3}{2}} + 6 x) d x

(2 x - 1) d x + (3 y + 7) d y = 0

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