The value of the integral `overset(1)underset(-1)int (x-[2x])`dx,is

The value of the integral overset(pi)underset(0)int log(1+cos x)dx is

The value of the integral int_0^1 x(1-x)^n dx=

The value of the integral int_(-1)^(1) sin^(11)x" dx" is

The value of the integral int_(0)^(1) cot^(-1) (1-x+x^(2))dx , is

The value of the integral int_(0)^(1)xcot^(-1)(1-x^(2)+x^(4)) dx is

The value of the integral int_(1)^(3)|(x-1)(x-2)|dx is

Let [t] denote the greatest integer le t. Then the value of 8 underset(-1/2)overset(1)int [2x]+|x| dx is ____________