consider the function f(x) = 9/x^3 -10/x^7 let F(x) be the antiderivatice of f(x) with F(1)=)

Question

then F(x)=

Answer 1

f(x) = 9/x^3 -10/x^7
= 9x^-3 - 10x^-7

If F'(x) = f(x)
then
F(x) = (9/-4)x^-4 - (10/-8)x^-8 + c
= (-9/4)(1/x^4) + (5/4)(1/x^8) + c

You have F(1) = ), since the ) is on the same key as 0, I will assume you meant:
F(1) = 0

0 = -9/4 + 5/4 + c
c = 1

F(x) = (-9/4)(1/x^4) + (5/4)(1/x^8) + 1

If I misunderstood make the necessary repairs.