tan^(-1)(a)/(x)+log sqrt((x-a)/(x+a))

log(sqrt(x)+1/sqrt(x))

The value of int((1+logx))/sqrt((x^x)^2-1)dx is (A) sec^-1(x^x)+c (B) tan^-1(x^x)+c (C) log(x+sqrt((x^x)^2-1))+c (D) none of these

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

f(x)=2x-tan^(-1)x-log(x+sqrt(1+x^(2)))(x>0) is increasing in

If f(x)=2x-tan^(-1) x-log (x+sqrt(x^(2)+1)) , then show that f(x) steadily increases as x increases from zero to positive infinity and hence deduce that, 2x gt tan^(-1) x+log (x+sqrt(x^(2)+1))

The greatest value of the function f(x)=tan^(-1)x-(1)/(2)log x in [(1)/(sqrt(3)),sqrt(3)] is

If y=log(x^(2)+x+1)/(x^(2)-x+1)+(2)/(sqrt(3))tan^(-1)((sqrt(3)x)/(1-x^(2))), find (dy)/(dx)

int_(1)^(7)(log sqrt(x))/(log sqrt(8-x)+log sqrt(x))dx=

int_(1)^(7)(log sqrt(x))/(log sqrt(8-x)+log sqrt(x))dx=