Integral of 10+0.02*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:

      $$\int \frac{x}{50}\, dx = \frac{\int x\, dx}{50}$$

      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: $\frac{x^{2}}{100}$

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

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

   The result is: $\frac{x^{2}}{100} + 10 x$

2. Now simplify:

   $$\frac{x \left(x + 1000\right)}{100}$$

3. Add the constant of integration:

   $$\frac{x \left(x + 1000\right)}{100}+ \mathrm{constant}$$

The answer is:

$$\frac{x \left(x + 1000\right)}{100}+ \mathrm{constant}$$