`f(x)=int_1^x(tan^(-1)(t))/t dt , x in R^+,` then find the value of `f(e^2)-f(1/(e^2))`

For x >0,l e tf(x)=int_1^x(logt)/(1+t)dtdot Find the function f(x)+f(1/x) and find the value of f(e)+f(1/e)dot

If f'(x)=f(x)+int_(0)^(1)f(x)dx ,given f(0)=1 , then the value of f(log_(e)2) is

If int_(0)^(x) f ( t) dt = x + int_(x)^(1) tf (t) dt , then the value of f(1) is

If f(x)=int_(2)^(x)(dt)/(1+t^(4)) , then

Iff(x)=e^(g(x))a n dg(x)=int_2^x(tdt)/(1+t^4), then find the value of f^(prime)(2)

If int_(sinx)^(1)t^(2)f(t)dt=1-sinx, xepsilon(0,(pi)/2) then find the value of f(1/(sqrt(3)))

If f(x)=inte^(x)(tan^(-1)x+(2x)/((1+x^(2))^(2)))dx,f(0)=0 then the value of f(1) is

Let f(x)=int_(2)^(x)f(t^(2)-3t+4)dt . Then

Let f(x)=1/x^2 int_0^x (4t^2-2f'(t))dt then find f'(4)

Let f(x)=int_(1)^(x)(3^(t))/(1+t^(2))dt , where xgt0 , Then