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

x \to 0 lim (- e^{\frac{1}{x}})

x \to 2 lim (\frac{x ^{2} - 1}{x + 1})

12 - 8 x + x^{2}

y = \frac{1}{1 - 8 x}, - 10 \leq x \leq 0

\int 5 \frac{sin ( 2 x )}{sin ( x )} 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