If `f(x)=int_(1)^(x)(e^t)/(1+t^(2))dt,AA x>0`, then `f'(t)` is equal to

If f(x)=int_(1)^(x)(logt)/(1+t+t^(2)) , AAx ge 1 , then f(2) is equal to

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

f(x) = int_(x)^(x^(2))(e^(t))/(t)dt , then f'(t) is equal to : (a) 0 (b) 2e (c) 2e^2 -2 (d) e^2-e

If f(x)=int_(1)^(x) (log t)/(1+t) dt"then" f(x)+f((1)/(x)) is equal to

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

Statement-1: If f(x)=int_(1)^(x) (log_(e )t)/(1+t+t^(2))dt , then f(x)=f((1)/(x)) for all x gr 0 . Statement-2:If f(x) =int_(1)^(x) (log_(e )t)/(1+t)dt , then f(x)+f((1)/(x))=((log_(e )x)^(2))/(2)

If f(x) = int_(0)^(x)(2cos^(2)3t+3sin^(2)3t)dt , f(x+pi) is equal to :

If f(x)=int_(x^2)^(x^2+1)e^(-t^2)dt , then f(x) increases in

If f(x)=int_(1)^(x)(logt)(1+t+t^(2))dt AAxge1 , then prove that f(x)=f(1/x) .

If f((1)/(x)) +x^(2)f(x) =0, x gt0 and I= int_(1//x)^(x) f(t)dt, (1)/(2) le x le 2x , then I is equal to