Integral of 2*x^2-3*x+5 dx

1. Integrate term-by-term:

   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:

         $$\int \left(- 3 x\right)\, dx = - 3 \int x\, dx$$

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

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

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

      $$\int 5\, dx = 5 x$$

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

2. Now simplify:

   $$\frac{x \left(4 x^{2} - 9 x + 30\right)}{6}$$

3. Add the constant of integration:

   $$\frac{x \left(4 x^{2} - 9 x + 30\right)}{6}+ \mathrm{constant}$$

The answer is:

$$\frac{x \left(4 x^{2} - 9 x + 30\right)}{6}+ \mathrm{constant}$$