Integral of 4x√1-2xdx dx

1. Integrate term-by-term:

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

      $$\int \left(- 2 x\right)\, dx = - 2 \int x\, dx$$

      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: $- x^{2}$

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

      $$\int \sqrt{1} \cdot 4 x\, dx = \int 4 x\, dx$$

      1. Don't know the steps in finding this integral.

         But the integral is

         $$2 x^{2}$$

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

   The result is: $x^{2}$

2. Add the constant of integration:

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

The answer is:

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