if fx 14x4x find fxSolutionYou have already given fx 14x4x

if f\'(x)= (1+4x^4)/x find f(x)

Solution

You have already given

f\'(x) = (1+4x^4)/x.

=> f\'(x) = 1/x + 4x^4/x

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

Taking integrals

f(x) = Int [ 1/x] + Int [ 4x^3]

=> ln x + (4/4)x^4

=> ln x + x^4

The required result in ln x + x^4