Assignment:
Given ( INTEGRAL ln square(x)dx, as x from n to n+1 ) = ( INTEGRAL ln square (n+x)dx, as x from 0 to 1 ) = ( INTEGRAL [[ln(n+x) - ln(x) + ln(n)]square] dx, as x from 0 to 1 ),
(a) Verify that ( LIMIT (n/ln(n)) [INTEGRAL (ln square (x)dx) - (ln square (n))] as n approach to the infinity ) = 1
(b) Compute LIMIT ((n square)/ln(n)) [ INTEGRAL ln square (x)dx - ln square (n) - ((ln(n))/n)]
Provide complete and step by step solution for the question and show calculations and use formulas.