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

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

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integral of (x^2+x^3)

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

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

Solution steps

\int x^{2} + x^{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 x^{2} d x + \int x^{3} d x

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

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

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

Add a constant to the solution

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

\frac{d x}{d t} = 2 x - x^{2}

\frac{\partial}{\partial x} (3 x - (\frac{3}{4} x + \frac{1}{4} y)^{2})

x \frac{d y}{d x} + (1 + x) y = e^{- x} sin (2 x)

\frac{d y}{d x} = - 1 + (2 x + y)^{2}

\frac{\partial}{\partial x} (4 x e^{x y})

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