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

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

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integral of (kx)/2-x^2

\int \frac{k x}{2} - x^{2} d x

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

Solution steps

\int \frac{k x}{2} - 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 \frac{k x}{2} d x - \int x^{2} d x

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

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

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

Add a constant to the solution

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

x \to \infty lim (0.5 x^{2})

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

x \to 0 lim (4 x + 48)

- 5 (t - 4)

\frac{d}{d x} (4 x^{2 π})

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