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

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

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integral of (x^2-x+2)

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

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

Solution steps

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

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

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

\int e^{- 2 t} + e^{2 t} + 2 d t

f (x) = (3 x^{2})^{2 x} (x^{2} + 2 x)^{2}

y^{^{''}} - 6 y^{^{'}} + 2 y = 0, y (0) = 0, y^{^{'}} (0) = 9

\frac{d y}{d t} = \frac{1}{5} t

y^{^{''}} - 0.2 y^{^{'}} + 0.01 y = 0, y (0) = 12, y^{^{'}} (0) = b

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