What is the integral of 10x-3x^2-x^3 ?

The integral of 10x-3x^2-x^3 is 5x^2-x^3-(x^4)/4+C

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integral of 10x-3x^2-x^3

\int 10 x - 3 x^{2} - x^{3} d x

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

Solution steps

\int 10 x - 3 x^{2} - x^{3} 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 10 x d x - \int 3 x^{2} d x - \int x^{3} d x

\int 10 x d x = 5 x^{2}

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

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

= 5 x^{2} - x^{3} - \frac{x ^{4}}{4}

Add a constant to the solution

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

x (\frac{d y}{d x}) + 2 y = 0

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

x \to 5 - lim (\frac{2}{( x - 5 )})

3 x^{2} e^{x} + e^{x} (x^{3} + 5)

y e^{2 x} d x - (4 + e^{2 x}) d y = 0

What is the integral of 10x-3x^2-x^3 ?
The integral of 10x-3x^2-x^3 is 5x^2-x^3-(x^4)/4+C