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

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

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

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

\int \frac{x}{( 4 x ^{2} + 3 ) ^{6}} d x

t an g e n t \frac{3}{2 3 x + 7}, at x = 6

\frac{d}{d x} (x^{2} arctan (x))

\frac{2 d y}{d x} + 5 y = 4

x \to 0 lim (\frac{1}{3})

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