What is the integral of-2x+18x^2-4x^3+C ?

The integral of-2x+18x^2-4x^3+C is -x^2+6x^3-x^4+Cx+C

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integral of-2x+18x^2-4x^3+C

\int - 2 x + 18 x^{2} - 4 x^{3} + C d x

- x^{2} + 6 x^{3} - x^{4} + C x + C

Solution steps

\int - 2 x + 18 x^{2} - 4 x^{3} + C 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 18 x^{2} d x - \int 4 x^{3} d x + \int C d x

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

\int 18 x^{2} d x = 6 x^{3}

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

\int C d x = C x

= - x^{2} + 6 x^{3} - x^{4} + C x

Add a constant to the solution

= - x^{2} + 6 x^{3} - x^{4} + C x + C

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

\frac{d}{d x} (2 x x sin (x))

\int (2 cos (x))^{2} d x

\frac{\partial}{\partial y} (5)

f (x) = - x^{2} + x, (- 1, - 2)

What is the integral of-2x+18x^2-4x^3+C ?
The integral of-2x+18x^2-4x^3+C is -x^2+6x^3-x^4+Cx+C