A tank contains 168.439 gallons of water at time t=0 hours. Water is pumped into the tank at a rate of 4 cos(t^2 +4)+6 gallons per hour. At t=3 hours, a valve in the bottom of the tank is opened, and water begins to flow out of the tank at a rate of -5 ln (t^2+1)24 gallons per hour. At time t=8, how much water is in the tank?