Evaluate: `int_1^(e^6)[(logx)/3]dx ,w h e r e[dot]` denotes the greatest integer function.

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

The value of int_(1)^(e^(6)) [(log x)/(3)] dx (where [.] denotes the greatest integer function) is (e^(a)-e^(b)) then the value of (a)/(b) is

Evaluate: int_(-5)^(5)x^(2)[x+(1)/(2)]dx (where [.] denotes the greatest integer function).

Evaluate: int_(-100)^(100)[tan^(-1)x]dx ,w h e r e[x] represents greatest integer function.

Evaluate int_(0)^(oo)[(3)/(x^(2)+1)]dx where [.] denotes the greatest integer function.

int_(0)^(5)e^([x])dx is (where [.] denotes the greatest integer function)

Evaluate: int_((pi)/(2))^(2 pi)[cot^(-1)]dx, where [.] denotes the greatest integer function

The value of int_(e)[log_(pi)x]dx is (where [.] denotes the greatest integer function)