Question #1983

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)=

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

G(x)=

Expert's answer

g(x) = 6/x^{7} - 4x^{3}/x^{7} + 3x^{7}/x^{7} = 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

G(x) = int(g(x), dx) = -6/6 x

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