Integral of (2x^2-10x+8) dx

1. Integrate term-by-term:

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

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

      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: $\frac{2 x^{3}}{3}$

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

      $$\int \left(- 10 x\right)\, dx = - \int 10 x\, dx$$

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

         $$\int 10 x\, dx = 10 \int x\, dx$$

         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: $5 x^{2}$

      So, the result is: $- 5 x^{2}$

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

      $$\int 8\, dx = 8 x$$

   The result is: $\frac{2 x^{3}}{3} - 5 x^{2} + 8 x$

2. Now simplify:

   $$\frac{x \left(2 x^{2} - 15 x + 24\right)}{3}$$

3. Add the constant of integration:

   $$\frac{x \left(2 x^{2} - 15 x + 24\right)}{3}+ \mathrm{constant}$$

The answer is:

$$\frac{x \left(2 x^{2} - 15 x + 24\right)}{3}+ \mathrm{constant}$$