The value of integral `underset(a)overset(b)int(|x|)/(x)dx`, `a lt b` is :

The value of integral underset(2)overset(4)int(dx)/(x) is :-

The integral underset(1)overset(5)int x^(2)dx is equal to

The value of integral int_(a)^(b)(|x|)/(x)dx , a lt b is :

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

Let f(x) be a continuous function such that f(a-x)+f(x)=0 for all x in [0,a] . Then, the value of the integral overset(a)underset(0)int (1)/(1+e^(f(x)))dx is equal to

The value of the integral underset(-1)overset(3 )int ("tan"^(1)(x)/(x^(2)+1)+"tan"^(-1)(x^(2)+1)/(x))dx is equal to

The value of the integral overset(1)underset(0)int e^(x^(2))dx lies in the integral

The value of the integral underset(e^(-1))overset(e^(2))int |(log_(e)x)/(x)|dx is

The value of the integral overset(e )underset(1//e)int |logx|dx , is

The value of the integral overset(pi)underset(0)int (sin k x)/(sin x)dx (k is an even integer) is equal to