sir , can you please help me to solve the question integral part of ^​ ​( 2^1/2 ​+1 ) ^​6

Since this is a constant value; its inetgral will be (2^(1/2) + 1)^6 ×(x). Unlike derivatives integrating a constant value gives the same value multiplied with `x` or the parameter used for integrating the function. If the function had been (x^(1/2) +1)^6 we would have used binomial expansion. Hope this solves your doubt