What is the integral of 2+6x-3x^2 ?

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

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integral of 2+6x-3x^2

\int 2 + 6 x - 3 x^{2} d x

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

Solution steps

\int 2 + 6 x - 3 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 2 d x + \int 6 x d x - \int 3 x^{2} d x

\int 2 d x = 2 x

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

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

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

Add a constant to the solution

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

\int \frac{3 x ^{2}}{x ^{2} + 2 x + 1} d x

x \to 0 lim (\frac{x ^{2}}{x})

\frac{d}{d x} (\frac{1}{x + x})

\frac{125}{x ^{2} + 49}

\int x^{2} 4 x + 6 d x