If I have the marginal cost function for producing the xth box of lightbulb as 10+ ((ln(x+1))/(x+1)^2) and know the fixed cost to be 3000 dollars, to find the total cost of x boxes, would I use the fixed cost to have a point at (3000,0) in order to find K so I can find the complete antiderivative function?
yes. But that does not mean that C=3000 in
∫(10+ ((ln(x+1))/(x+1)^2)) dx = f(x) + C