It is estimated that x years from now, the value V(x) of an acre of farmland will be increasing at the rate of:

Question

V'(x)= 0.4x^3/sqrroot(0.2x^4+8000

dollars per year. The land is currently worth $500 per acre.

A. Find V(x)
b. How much will the land be worth in 10 years?

You want the integral of
V'(x) = 0.4 x^3/(sqrt 0.2 x^4 +8000)
such that V(0) = 500

The integral is a difficult one and is not in my integal tables. I would use numerical integration. Sorry I cannot be of more help