Evaluate `int_(1)^(e^(6))[(logx)/(3)]dx`, where `[**]` denotes the greatest integer function.

The value of int_(0)^(pi)[2sinx]dx , where [**] denoted the greatest integer function, is a) pi/3 b) (2pi)/(3) c) pi/6 d)None of these

Evaluate int(1)/(1+e^(-x))dx .

Find the solution of [x]^2-5[x]+6=0 ,where [] denotes the greatest integer function.