∫x−−√dx

The integral of the function x - sqrt(x) with respect to x can be solved as follows:

Step 1: Break the integral into two separate integrals. ∫x dx - ∫sqrt(x) dx

Step 2: Solve each integral separately.

The integral of x with respect to x is (1/2)x^2.

The integral of sqrt(x) with respect to x is (2/3)x^(3/2).

Step 3: Combine the results from step 2. (1/2)x^2 - (2/3)x^(3/2)

So, ∫x - sqrt(x) dx = (1/2)x^2 - (2/3)x^(3/2) + C, where C is the constant of integration.