What is the integral of-2x+9x^2-4x^3+14 ?

The integral of-2x+9x^2-4x^3+14 is -x^2+3x^3-x^4+14x+C

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integral of-2x+9x^2-4x^3+14

\int - 2 x + 9 x^{2} - 4 x^{3} + 14 d x

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

Solution steps

\int - 2 x + 9 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 9 x^{2} d x - \int 4 x^{3} d x + \int 14 d x

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

\int 9 x^{2} d x = 3 x^{3}

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

\int 14 d x = 14 x

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

Add a constant to the solution

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

10 e^{x^{2}} x

\frac{\partial}{\partial x} ((x^{2} + y^{2} + z^{2})^{\frac{n}{2}})

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

\frac{\partial}{\partial x} (2 1 - y^{2})

(14 + x) \frac{d y}{d x} = 5 y

What is the integral of-2x+9x^2-4x^3+14 ?
The integral of-2x+9x^2-4x^3+14 is -x^2+3x^3-x^4+14x+C