What is the integral of-2x+12x^2-4x^3+14 ?

The integral of-2x+12x^2-4x^3+14 is -x^2+4x^3-x^4+14x+C

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integral of-2x+12x^2-4x^3+14

\int - 2 x + 12 x^{2} - 4 x^{3} + 14 d x

- x^{2} + 4 x^{3} - x^{4} + 14 x + C

Solution steps

\int - 2 x + 12 x^{2} - 4 x^{3} + 14 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 x d x + \int 12 x^{2} d x - \int 4 x^{3} d x + \int 14 d x

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

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

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

\int 14 d x = 14 x

= - x^{2} + 4 x^{3} - x^{4} + 14 x

Add a constant to the solution

= - x^{2} + 4 x^{3} - x^{4} + 14 x + C

\int \frac{2 sin ^{3} ( x )}{x} d x

\int \frac{44 - x}{x ^{2} + 2 x - 24} d x

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

1 + e^{4 t}

x \to - 4 lim (8 x + 3)

What is the integral of-2x+12x^2-4x^3+14 ?
The integral of-2x+12x^2-4x^3+14 is -x^2+4x^3-x^4+14x+C