What is the integral of (x^2-sqrt(x)+3) ?

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

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integral of (x^2-sqrt(x)+3)

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

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

Solution steps

\int x^{2} - x + 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 x^{2} d x - \int x d x + \int 3 d x

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

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

\int 3 d x = 3 x

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

Add a constant to the solution

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

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