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

The integral of (-(x^3)/3-x^2+4/3) is -(x^4}{12}-\frac{x^3)/3+4/3 x+C

Popular >

integral of (-(x^3)/3-x^2+4/3)

\int (- \frac{x ^{3}}{3} - x^{2} + \frac{4}{3}) d x

- \frac{x ^{4}}{12} - \frac{x ^{3}}{3} + \frac{4}{3} x + C

Solution steps

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

\int \frac{x ^{3}}{3} d x = \frac{x ^{4}}{12}

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

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

= - \frac{x ^{4}}{12} - \frac{x ^{3}}{3} + \frac{4}{3} x

Add a constant to the solution

= - \frac{x ^{4}}{12} - \frac{x ^{3}}{3} + \frac{4}{3} x + C

f (x) = e^{x}, x = 0

\frac{d}{d x} (A e^{3 x})

f (x) = 5 x^{3}, - 10, 15, at x = 0

\frac{\partial}{\partial x} (1 - x^{2} - y^{2})

\int_{- 2}^{0} \frac{y}{2} + y + 3 d y

What is the integral of (-(x^3)/3-x^2+4/3) ?
The integral of (-(x^3)/3-x^2+4/3) is -(x^4}{12}-\frac{x^3)/3+4/3 x+C