What is the integral of-2x+15x^2-4x^3+C ?

The integral of-2x+15x^2-4x^3+C is -x^2+5x^3-x^4+Cx+C

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integral of-2x+15x^2-4x^3+C

\int - 2 x + 15 x^{2} - 4 x^{3} + C d x

- x^{2} + 5 x^{3} - x^{4} + C x + C

Solution steps

\int - 2 x + 15 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 15 x^{2} d x - \int 4 x^{3} d x + \int C d x

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

\int 15 x^{2} d x = 5 x^{3}

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

\int C d x = C x

= - x^{2} + 5 x^{3} - x^{4} + C x

Add a constant to the solution

= - x^{2} + 5 x^{3} - x^{4} + C x + C

y^{^{'}} + (\frac{7 x}{x ^{2} + 1}) y = \frac{7 x}{x ^{2} + 1}

\frac{( ( \frac{4}{x} ) ^{2} )}{1 - \frac{4}{x}}

\frac{d}{d x} (4 + 7 x)

\int_{0}^{1} 5^{4 x} d x

\frac{\partial}{\partial x} (y sin (2 x))

What is the integral of-2x+15x^2-4x^3+C ?
The integral of-2x+15x^2-4x^3+C is -x^2+5x^3-x^4+Cx+C