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

Evaluate: int_(-5)^5x^2[x+1/2]dx(w h e r e[dot] denotes the greatest integer function).

Evaluate: int_0^((5pi)/(12))[tanx]dx , where [dot] denotes the greatest integer function.

Prove that int_0^oo[cot^(-1)x]dx ,w h e r e[dot] denotes the greatest integer function.

Evaluate: int_0^2[x^2-x+1]dx ,w h e r e[dot] denotos the greatest integer function.

Evaluate: int_0^(2pi)[sinx]dx ,w h e r e[x] denotes the greatest integer function.

Evaluate int_(1)^(e)(1+logx)/(x)dx

Evaluate int_(-1)^(3)(x-[x])dx ,where [.] denotes the greatest integer function.

Evaluate int_(-1)^(3)(x+[x])dx ,where [.] denotes the greatest integer function.

Evaluate int_(-1)^(1)(x+[x])dx ,where [.] denotes the greatest integer function.

The integral int_0^(1. 5)[x^2]dx ,w h e r e[dot] denotoes the greatest integer function, equals ...........