Integral of 3x^3+const dx

1. Integrate term-by-term:

   1. The integral of a constant is the constant times the variable of integration:

      $$\int c\, dx = c x$$

   1. The integral of a constant times a function is the constant times the integral of the function:

      $$\int 3 x^{3}\, dx = 3 \int x^{3}\, dx$$

      1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$:

         $$\int x^{3}\, dx = \frac{x^{4}}{4}$$

      So, the result is: $\frac{3 x^{4}}{4}$

   The result is: $c x + \frac{3 x^{4}}{4}$

2. Now simplify:

   $$x \left(c + \frac{3 x^{3}}{4}\right)$$

3. Add the constant of integration:

   $$x \left(c + \frac{3 x^{3}}{4}\right)+ \mathrm{constant}$$

The answer is:

$$x \left(c + \frac{3 x^{3}}{4}\right)+ \mathrm{constant}$$