If F(x)`=int_(x^(2))^(x^(3)) log t dt (x gt 0)`, then F'(x) equals

If F(x) = int_(x^(2))^(x^(3)) log t dt ,( t gt 0) then F^(')(x) is equal to

Find the derivative with respect to x of the following functions : (a) F(x) = int_(x^(2))^(x^(3)) "In t dt " (x gt 0) (b) f(x) = int_(1//x)^(sqrt(x)) cos (t^(2)) dt (x gt 0)

f(x) = int_(x)^(x^(2))(e^(t))/(t)dt , then f'(t) is equal to :

Let f (x)= int _(x^(2))^(x ^(3))(dt)/(ln t) for x gt 1 and g (x) = int _(1) ^(x) (2t ^(2) -lnt ) f(t) dt(x gt 1), then:

If f(x)= int_(x)^(x^(2))1/((log t)^2)dt ,x ne 1 then f(x)is monotomically

The derivative of f(x)=int_(x^(2))^(x^(3))(1)/(log_(e)(t))dt,(x>0), is

Let F(x) =f(x) +f((1)/(x)),"where" f(x)=int_(1)^(x) (log t)/(1+t) dt Then F (e) equals

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