`int_0^(102)(x-1)(x-2)..(x-100)xx(1/(x-1)+1/(x-2)+..1/(x-100))dx=101 !-100 !`

int_0^1(x^2-2)/(x^2+1)dx=?

int_((1)/(2))^(2)(1)/(x)sin^(101)(x-(1)/(x))dx=

Let f(x)=(a^(x))/(a^(x)+sqrt(a)),a>1 and int_(0)^(2)(f((1)/(100))+f((2)/(100))+f((3)/(100))+...+f((99)/(100)))*dx=k times11 then k=

The vlaue of ((5050)int_(0)^(1)(1-x^(50))^(100)dx)/(int_(0)^(1) (1-x^(50))^(100)dx) , is

(lim)_(x->0)([100(sin^(-1)\ x)/x]+[100(tan^(-1)x)/x])=

lim_(x rarr1)[(x^(2)+1)/(x+100)]

Evaluate : int_0^(1) ((1)/(1+x^(2))) sin^(-1)""((2x)/(1+x^(2))) dx

int_0^1 tan^1x/(1+x^2)dx