Anti derivative for given condition

Question

4x^-3 + 7x^-1 -1; y(1)=3

Answer 1

f(x) = 4/x^3 + 7/x -1

F(x) = -2/x^2+ 7lnx -x + k where k = a constant, solve for k by plugging in x=1

F(1) = -2/1^2 +7ln1 - 1 + k = 3

-2 + 7(0) - 1 + k = 3

k = 6

F(x) = y = -2/x^2 + 7lnx - x + 6