What is the integral of 1/2 x^2-2x+6 ?

The integral of 1/2 x^2-2x+6 is (x^3)/6-x^2+6x+C

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integral of 1/2 x^2-2x+6

\int \frac{1}{2} x^{2} - 2 x + 6 d x

\frac{x ^{3}}{6} - x^{2} + 6 x + C

Solution steps

\int \frac{1}{2} x^{2} - 2 x + 6 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 \frac{1}{2} x^{2} d x - \int 2 x d x + \int 6 d x

\int \frac{1}{2} x^{2} d x = \frac{x ^{3}}{6}

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

\int 6 d x = 6 x

= \frac{x ^{3}}{6} - x^{2} + 6 x

Add a constant to the solution

= \frac{x ^{3}}{6} - x^{2} + 6 x + C

\frac{3}{s} + \frac{24}{s ^{2}}

\frac{d ^{2} y}{d x} + 4 \frac{d y}{d x} - 12 y = 0

\frac{\partial}{\partial x} (x sin (8 x^{2} y))

\frac{- 60}{- 2 + 5 s}

(\frac{e ^{x} + e ^{- x}}{2})^{^{'}}

What is the integral of 1/2 x^2-2x+6 ?
The integral of 1/2 x^2-2x+6 is (x^3)/6-x^2+6x+C