Let `f:R rarr[0,oo)` be a differentiable function so that `f'(x)` is continuous function then `int((f(x)-f'(x))e^(x))/((e^(x)+f(x))^(2))dx` is equal to

I=int_(0)^(2)(e^(f(x)))/(e^(f(x))+e^(f(2-x)))dx is equal to

If int f(x)dx=F(x),f(x) is a continuous function,then int(f(x))/(F(x))dx equals

If f is continuously differentiable function then int_(0)^(2.5) [x^2] f'(x) dx is equal to

Let f(x) be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt then int_(0)^(1)f(x)dx=

Let f(x) be the continuous function such that f(x)= (1-e^(x))/(x) for x!=0 then

Let f is a differentiable function such that f'(x) = f(x) + int_(0)^(2) f(x) dx, f(0) = (4-e^(2))/(3) , find f(x).

Let f:(0, oo)rarr(0, oo) be a differentiable function such that f(1)=e and lim_(trarrx)(t^(2)f^(2)(x)-x^(2)f^(2)(t))/(t-x)=0 . If f(x)=1 , then x is equal to :

let f:R rarr R be a continuous function defined by f(x)=(1)/(e^(x)+2e^(-x))

if f be a differentiable function such that f(x) =x^(2)int_(0)^(x)e^(-t)f(x-t). dt. Then f(x) =

Let f be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt then prove that f(x)=(x^(3))/(3)+x^(2)