`e^(tan^(-1)x)log(tanx)`

e^(tan^(-1)x)log(tan x)

Let f(x)=(lim)_(xvecoo)(tan^(-1)(tanx))/(1+((log)_e x)^n),x!=(2n+1)pi/2 then AA1 e ,f(x) is a constant function

Integration of (1)/(1+((log)_(e)x)^(2)) with respect to (log)_(e)x is ((tan^(-1)((log)_(e)x))/(x)+C(b)tan^(-1)((log)_(e)x)+C(c)(tan^(-1)x)/(x)+C(d) none of these

The value of int_(1)^(e)((tan^(-1)x)/(x)+(log x)/(1+x^(2)))dx is tan e(b)tan^(-1)e tan^(-1)((1)/(e))(d) none of these

If f(x)=(log_(cotx)tanx)(log_(tanx)cotx)+tan^(-1)""(4x)/(4-x^2) then 2f'(2) is equal to

int(sec^(2)xdx)/(log (tan x)^(tanx)) =

int(e^(ln tan^(-1)x))/(1+x^(2))dx

int(x^(3)-1)/(x^(3)+x)dx is equal to a) x-log_(e)|x|+log_(e)(x^(2)+1)-tan^(-1)x+C b) x-log_(e)|x|+1/2log_(e)(x^(2)+1)-tan^(-1)x+C c) x+log_(e)|x|+1/2log_(e)(x^(2)+1)+tan^(-1)x+C d)None of these

Let f(x)=lim_(nrarroo) (tan^(-1)(tanx))/(1+(log_(x)x)^(n)),x ne(2n+1)(pi)/(2) then