What is the integral of sqrt(x)-x^2 ?

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

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integral of sqrt(x)-x^2

\int x - x^{2} d x

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

Solution steps

\int x - x^{2} 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 x d x - \int x^{2} d x

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

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

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

Add a constant to the solution

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

\frac{d}{d x} (x^{3} + 2 x + 3)

f (x) = 4 x^{2} + 9 x

\int_{- 2}^{1} 1 + (- 3)^{2} d x

\int cos^{2} (x) sin^{4} (x) d x

\int e^{- s x} \cdot x^{2} d x

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