Answer to Question #1983 in Calculus for Bindu

Question

Find the most general antiderivative of the function. Use C for any needed constant. (Check your answer by differentiation.) (x>0)
g(x) = (6 - 4 x^3 + 3 x^(7))/x^(7)

G(x)=

Answer 1

g(x) = 6/x⁷ - 4x³/x⁷ + 3x⁷/x⁷ = 6x^-7 - 4x^-4 + 3

G(x) = int(g(x), dx) = -6/6 x^-6 + 4/3 x^-3 + 3x + C = - x^-6 +4/3 x^-3 + 3x + C