The capitalized cost of an asset is the total of the original cost and the present value of all future “renewals” or replacements. This concept is useful, for example, when you are selecting equipment that is manufactured by several different companies. Suppose that a corporation computes the present value of future expenditures using an annual interest rate r, with continuous compounding of interest. Assume that the original cost of an asset is $80,000 and the annual renewal expense will be $50,000, spread more-or-less evenly throughout each year, for a large but indefinite number of years. Find a formula involving an integral that gives the capitalized cost of the asset.