Let `f(0)=0a n dint_0^2f^(prime)(2t)e^(f(2t))dt=5.t h e nv a l u eoff(4)i s` log 2 (b) log 7 (c) log 11 (d) log 13

I=int_(0)^(-1)(t ln t)/(sqrt(1-t^(2)))dt=

Let f(x)=int_(0)^(x)e^(t)(t-1)(t-2)dt. Then, f decreases in the interval

Let f(x)=int_(0)^(oo)(e^(-xt))/(1+t^(2))dt, then value of prime 'f''((1)/(4))+f((1)/(4))=

If f(x)=int_(1)^(x)(ln t)/(1+t)dt, then

Let f,g:(0,oo)rarr R be two functions defined by f(x)=int_(-x)^(x)(|t|-t^(2))e^(-t^(2))dt and g(x)=int_(0)^(x^(2))t^(1/2)e^(-t)dt .Then,the value of 9(f(sqrt(log_(e)9))+g(sqrt(log_(e)9))) is equal to

let f(x)=(ln(x^(2)+e^(x)))/(ln(x^(4)+e^(2x))) then lim_(x rarr oo)f(x) is

(d)/(dt)log(1+t^(2))