What is the integral of (x^3+1.8x^2-2.4x) ?

The integral of (x^3+1.8x^2-2.4x) is 0.25x^4+0.6x^3-1.2x^2+C

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integral of (x^3+1.8x^2-2.4x)

\int (x^{3} + 1.8 x^{2} - 2.4 x) d x

0.25 x^{4} + 0.6 x^{3} - 1.2 x^{2} + C

Solution steps

\int x^{3} + 1.8 x^{2} - 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 1.8 x^{2} d x - \int 2.4 x d x

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

\int 1.8 x^{2} d x = 0.6 x^{3}

\int 2.4 x d x = 1.2 x^{2}

= \frac{x ^{4}}{4} + 0.6 x^{3} - 1.2 x^{2}

Simplify

= 0.25 x^{4} + 0.6 x^{3} - 1.2 x^{2}

Add a constant to the solution

= 0.25 x^{4} + 0.6 x^{3} - 1.2 x^{2} + C

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

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

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\int \frac{5}{x ^{5}} d x

What is the integral of (x^3+1.8x^2-2.4x) ?
The integral of (x^3+1.8x^2-2.4x) is 0.25x^4+0.6x^3-1.2x^2+C