The value of `lim_(a rarr oo)(1)/(a^(2))int_(0)^(a)ln(1+e^(x))dx` equals

Let a in(0,(pi)/(2)) ,then the value of lim_(a rarr0)(1)/(a^(3))int_(0)^(a)ln(1+tan a tan x)dx is equal to

lim_(n rarr oo)(n)/(2^(n))int_(0)^(2)x^(n)dx equals

The value of lim_(x rarr oo)((ln x)^(2))/(x^(2)) is

The value of (lim_(x rarr0)(1)/(x^(6))int_(0)^(x^(2))sin(t^(2))dt) is equal to

The value of lim_(x rarr oo)x^(2)ln(x cot^(-1)x) is

lim_(x rarr0)(1)/(x^(2))int_(0)^(x)(tdt)/(t^(4)+1) is equal to

If a,b and c are real numbers then the value of lim_(t rarr0)ln((1)/(t)int_(0)^(t)(1+a sin bx)^((c)/(x))dx) equals

The value of lim_(x rarr0)(int_(0)^(x) xe^(t^(2))dt)/(1+x-e^(x)) is equal to

The value of lim_(x rarr0)int_(0)^(x)(t ln(1+t))/(t^(4)+4)dt