What is the integral of-x^3+5x^2-4x ?

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

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integral of-x^3+5x^2-4x

\int - x^{3} + 5 x^{2} - 4 x d x

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

Solution steps

\int - x^{3} + 5 x^{2} - 4 x 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 x^{3} d x + \int 5 x^{2} d x - \int 4 x d x

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

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

\int 4 x d x = 2 x^{2}

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

Add a constant to the solution

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

\frac{d}{d x} ((\frac{x}{3} + 1)^{\frac{3}{2}})

\int cos (x) (6 + 4 sin^{2} (x)) d x

\frac{\partial}{\partial x} (9 - 3 x^{2} - y^{2})

x \to 2 lim (3 - x^{2})

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