take x^n out of the bracket in the Denominator
it will become x^(-n-1) / (1 + x^-n )
Which is of the form f '(x) / f(x)
Put xn + 1 = t
=> n xn-1 dx = dt
=> dx / x = dt/n(t -1)
I = INTEG [ dt / nt(t-1) ]
= 1/n ln [(t-1)/t]
Therefore , I = 1/n ln [(xn) / (xn + 1 ) ]
take x^n out of the bracket in the Denominator
it will become x^(-n-1) / (1 + x^-n )
Which is of the form f '(x) / f(x)