Find the equation of the function f(x) if f'(x) = (x^3 - x) / 4x^4.

Given the derivative f'(x) = (x^3 -
x)/4x^4

Let us
simplify.

==> f'(x) = (x^3/4x^4) -
x/4x^4

==> f'(x) = (1/4x) -
1/4x^3

==> f'(x) =(1/4)[ 1/x -
x^-3)

Now we will
integrate.

==> f(x) = Int f'(x) = (1/4) * Int ( 1/x
- x^-3) dx

              = (1/4) [ lnx - x^-2/-2 ] +
C

             = (1/4) l lnx + 1/2x^2)  +
C

Then the function f(x) is given by : f(x) =
(1/4) *[ ln x + 1/2x^2] + C