The equation ∫ f(x)g(x) = ∫ f(x) * ∫ g(x) is incorrect. The derivative of the product f(x)g(x) is not equal to the product of their derivatives, as shown by the product rule. Instead, the correct derivative is (f(x)g(x))' = f'(x)g(x) + f(x)g'(x). Integration by parts is a method that can be applied to integrate products of functions. Understanding these principles is crucial for accurate integration techniques.