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

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

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integral of 6x^2-2x+1

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

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

Solution steps

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

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

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

\int 1 d x = x

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

Add a constant to the solution

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

n = 1 \sum \infty \frac{n}{n ^{3} + 3}

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