Calculus: Early Transcendentals, Chapter 4, 4.9, Section 4.9, Problem 14

The most general antiderivative F(t) of the function f(t) can be found using the following relation:
int f(t)dt = F(t) + c
int (3t^4 - t^3 + 6t^2)/(t^4)dt = int (3t^4)/(t^4)dt - int (t^3)/(t^4)dt + int 6t^2/(t^4) dt
You need to use the following formula:
int t^n dt = (t^(n+1))/(n+1)
int (3t^4)/(t^4)dt = int 3dt = 3t + c
int (t^3)/(t^4)dt = int (1/t) dt = ln |t| + c
int 6t^2/(t^4) dt = 6 int 1/(t^2) dt = -6/t + c
Gathering all the results yields:
int (3t^4 - t^3 + 6t^2)/(t^4)dt = 3t - ln |t| -6/t + c
Hence, evaluating the most general antiderivative of the function yields F(t) = 3t - ln |t| -6/t + c.