Help with math, please anyone

Question

Pumping stations deliver oil at the rate modeled by the function D, given by  with t measure in hours and and D(t) measured in gallons per hour. How much oil will the pumping stations deliver during the 4-hour period from t = 0 to t = 4? Please give it in 3 decimal places.

Answer 1

Integrating a rational function

(5t)/(1+3t) = 5/3 - 5/3(3t+1)

integrating: result is (5/3)[t- (1/3)ln(3t+1)] evaluated from 0 to 4

= (5/3)[4 - (ln13)/3] = 5.242 gallons