Integral of 15*x^2/2-2*x dx

1. Integrate term-by-term:

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

      $$\int \left(- 2 x\right)\, dx = - 2 \int x\, dx$$

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

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

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

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

      $$\int \frac{15 x^{2}}{2}\, dx = \frac{\int 15 x^{2}\, dx}{2}$$

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

         $$\int 15 x^{2}\, dx = 15 \int x^{2}\, dx$$

         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: $5 x^{3}$

      So, the result is: $\frac{5 x^{3}}{2}$

   The result is: $\frac{5 x^{3}}{2} - x^{2}$

2. Now simplify:

   $$\frac{x^{2} \left(5 x - 2\right)}{2}$$

3. Add the constant of integration:

   $$\frac{x^{2} \left(5 x - 2\right)}{2}+ \mathrm{constant}$$

The answer is:

$$\frac{x^{2} \left(5 x - 2\right)}{2}+ \mathrm{constant}$$