Integral of 10xy dx

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

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

   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: $5 x^{2} y$

2. Add the constant of integration:

   $$5 x^{2} y+ \mathrm{constant}$$

The answer is:

$$5 x^{2} y+ \mathrm{constant}$$