Consider the function f ( x ) = 8/ x 3 − 2 /x 5 . Let F ( x ) be the antiderivative of f ( x ) with F ( 1 ) = 0 . Then F ( x ) =

Question

Consider the function .Let  be the antiderivative of  with .Then 

Answer 1

The integral of 8/x^3 - 2/x^5 = -4/x^2 + 1/2x^4 + C

F(1) = 0 = -4/1^2 +1/2*1^4 + C = -4 +1/2 +C

0 = -3.5 + C

C = 3.5

F(X) = -4/x^2 + 1/2x^4 + 3.5

Answer 2

F(x) = ∫f(x)dx = ∫8/x³ - 2/x⁵dx = 8/(-4x⁴) - 2/(-6x⁶) + C

= -2/x⁴ + 1/(3x⁶) + C

If F(1) = -2 + 1/3 + C = 0 then C = 5/3

F(x) = -2/x⁴ + 1/(3x⁶) + 5/3