Find $\int(x+3)(x-7) d x$

Step 1 ：Given the integral to solve is \(\int(x+3)(x-7) dx\)

Step 2 ：First, we expand the expression inside the integral to get \(x^2 - 4x - 21\)

Step 3 ：Then, we integrate term by term to get \(\frac{x^3}{3} - 2x^2 - 21x\)

Step 4 ：Finally, we add the constant of integration, C, to get the final answer

Step 5 ：The integral of the function \((x+3)(x-7)\) with respect to x is \(\boxed{\frac{x^3}{3} - 2x^2 - 21x + C}\)