Consider the fuction f(x)=(9/x^3)-(7/x^7)

Question

Let F(x) be the antiderivative of f(x) with F(1)=0.

Then F(x)=

Answer 1

F(x) = 9∫x^-3dx - 7∫x^-7dx = -(9/2)x^-2 + (7/6)x^-6 + C

Since F(1) = 0, -9/2 + 7/6 + C = 0. So, C = 10/3.

F(x) = -(9/2)x^-2 + (7/6)x^-6 + 10/3