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

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

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integral of 12x^2+2x-6

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

4 x^{3} + x^{2} - 6 x + C

Solution steps

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

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

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

\int 6 d x = 6 x

= 4 x^{3} + x^{2} - 6 x

Add a constant to the solution

= 4 x^{3} + x^{2} - 6 x + C

\int 9 arctan (x) d x

\frac{\partial}{\partial y} (7 y - 5 x)

x \to \infty lim (lo g_{10} (2 x))

x \to - 1 lim (\frac{x ^{2} - x}{x + 1})

\frac{d}{d x} (9 sec (x))

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