Integral of (2-5*x)*i*n*x dx

1. Rewrite the integrand:

   $$x n i \left(2 - 5 x\right) = - 5 i n x^{2} + 2 i n x$$

2. Integrate term-by-term:

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

      $$\int \left(- 5 i n x^{2}\right)\, dx = - 5 i n \int x^{2}\, dx$$

      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: $- \frac{5 i n x^{3}}{3}$

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

      $$\int 2 i n x\, dx = 2 i n \int x\, dx$$

      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: $i n x^{2}$

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

3. Now simplify:

   $$\frac{i n x^{2} \left(3 - 5 x\right)}{3}$$

4. Add the constant of integration:

   $$\frac{i n x^{2} \left(3 - 5 x\right)}{3}+ \mathrm{constant}$$

The answer is:

$$\frac{i n x^{2} \left(3 - 5 x\right)}{3}+ \mathrm{constant}$$