$\int \frac{3}{6+3 x} d x, x \neq-2$

Step 1 ：This is a simple integral problem. The integral of a function f(x) is the area under the curve of the function from a certain point to another. In this case, we are asked to find the integral of the function f(x) = \(\frac{3}{6+3x}\).

Step 2 ：This is a simple rational function, and we can solve it by using the method of substitution. We can let u = 6 + 3x, then du = 3dx. The integral then becomes ∫du/u, which is a standard integral that equals to ln|u| + C, where C is the constant of integration.

Step 3 ：We then substitute u back to the original variable x to get the final answer. The output is the integral of the function, which is log(x + 2). This is the natural logarithm of (x + 2).

Step 4 ：This is the indefinite integral of the function, which means it represents a family of functions, each of which is a possible antiderivative of the original function. The '+ C' is omitted in the output, but it's understood to be there.

Step 5 ：The 'C' represents the constant of integration, which can be any constant number, and it comes from the fact that the derivative of a constant is zero.

Step 6 ：Final Answer: \(\boxed{\ln|x + 2| + C}\)