What is the integral of 12x^2+2x+1 ?

The integral of 12x^2+2x+1 is 4x^3+x^2+x+C

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integral of 12x^2+2x+1

\int 12 x^{2} + 2 x + 1 d x

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

Solution steps

\int 12 x^{2} + 2 x + 1 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 1 d x

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

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

\int 1 d x = x

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

Add a constant to the solution

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

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