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

The integral of (x^3)/3+2x-5 is (x^4)/(12)+x^2-5x+C

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integral of (x^3)/3+2x-5

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

\frac{x ^{4}}{12} + x^{2} - 5 x + C

Solution steps

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

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

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

\int 5 d x = 5 x

= \frac{x ^{4}}{12} + x^{2} - 5 x

Add a constant to the solution

= \frac{x ^{4}}{12} + x^{2} - 5 x + C

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

\frac{\partial}{\partial x} (sin (c x))

\frac{d}{d x} (\frac{x ^{3}}{3} - 5 x^{2} + 21 x + 1)

x \to 3 lim (- 6)

x \to 9 - lim (\frac{3}{x - 9})

What is the integral of (x^3)/3+2x-5 ?
The integral of (x^3)/3+2x-5 is (x^4)/(12)+x^2-5x+C