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

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

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integral of-2x+6x^2-4x^3+C

\int - 2 x + 6 x^{2} - 4 x^{3} + C d x

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

Solution steps

\int - 2 x + 6 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 6 x^{2} d x - \int 4 x^{3} d x + \int C d x

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

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

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

\int C d x = C x

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

Add a constant to the solution

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

\frac{\partial}{\partial y} (ln (1 + x y))

n = 1 \sum \infty \frac{1}{n} - \frac{1}{2 n + 1}

1 - x^{2}, 0

\frac{d}{d x} (2 - 3 x^{2})

f (x) = \frac{x ^{2}}{1 + 4 x}

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