What is the integral of (12x^2-6x+2) ?

The integral of (12x^2-6x+2) is 4x^3-3x^2+2x+C

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integral of (12x^2-6x+2)

\int (12 x^{2} - 6 x + 2) d x

4 x^{3} - 3 x^{2} + 2 x + C

Solution steps

\int 12 x^{2} - 6 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 12 x^{2} d x - \int 6 x d x + \int 2 d x

\int 12 x^{2} d x = 4 x^{3}

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

\int 2 d x = 2 x

= 4 x^{3} - 3 x^{2} + 2 x

Add a constant to the solution

= 4 x^{3} - 3 x^{2} + 2 x + C

\frac{\partial}{\partial y} (sin (x y) + x y cos (x y))

\frac{\partial}{\partial x} (x (x^{2} - 3 y^{2}))

x \to 0 lim (\frac{e ^{2 x - 1}}{tan ( x )})

4 e^{2 t}

y = 2 tan^{2} (2 x) - 1

What is the integral of (12x^2-6x+2) ?
The integral of (12x^2-6x+2) is 4x^3-3x^2+2x+C