Integral of 3*x^2-2/x^3 dx

1. Integrate term-by-term:

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

      $$\int 3 x^{2}\, dx = 3 \int x^{2}\, dx$$

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

         $$\int x^{2}\, dx = \frac{x^{3}}{3}$$

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

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

      $$\int \left(- \frac{2}{x^{3}}\right)\, dx = - \int \frac{2}{x^{3}}\, dx$$

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

         $$\int \frac{2}{x^{3}}\, dx = 2 \int \frac{1}{x^{3}}\, dx$$

         1. Don't know the steps in finding this integral.

            But the integral is

            $$- \frac{1}{2 x^{2}}$$

         So, the result is: $- \frac{1}{x^{2}}$

      So, the result is: $\frac{1}{x^{2}}$

   The result is: $x^{3} + \frac{1}{x^{2}}$

2. Now simplify:

   $$\frac{x^{5} + 1}{x^{2}}$$

3. Add the constant of integration:

   $$\frac{x^{5} + 1}{x^{2}}+ \mathrm{constant}$$

The answer is:

$$\frac{x^{5} + 1}{x^{2}}+ \mathrm{constant}$$