What is the integral of x^2(2x-5) ?

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

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integral of x^2(2x-5)

\int x^{2} (2 x - 5) d x

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

Solution steps

\int x^{2} (2 x - 5) d x

Expand

x^{2} (2 x - 5) : 2 x^{3} - 5 x^{2}

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

\int 2 x^{3} d x = \frac{x ^{4}}{2}

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

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

Add a constant to the solution

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

Q (x) = x^{4} + 8 x^{2} + 16

\int x^{2} e^{1 - x} d x

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

\int \frac{1}{49 + x ^{2}} d x

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

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