How would you integrate (2x-1) (6x+5) ? is there a product rule for integration?

No, there is not a product rule for integration.

To integrate (2x - 1) (6x + 5), start expanding the product:

(2x - 1) (6x + 5) = 12x^2 + 10x - 6x - 5 = 12x^2 + 4x - 5.

Now, I guess you know how to integrate that:

∫ (12x^2 + 4x - 5) dx = ∫12x^2 dx + ∫4x dx + ∫ (-5) dx = 4x^3 + 2x^2 - 5x + C