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)

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

If f(x)=tan^(-1)[(log((e )/(x^(2))))/(log (ex^(2)))]+tan^(-1)[(3+2 log x)/(1-6 log x)] then the value of f''(x) is

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))

Of f(x)=(2)/(sqrt(3))tan^(-1)((2x+1)/(sqrt(3)))-log(x^(2)+x+1)(lambda^(2)-5 lambda+3)x+10 is a decreasing function for all x in R, find the permissible values of lambda.

Of f(x)=2/(sqrt(3))tan^(-1)((2x+1)/(sqrt(3)))-log(x^2+x+1)(lambda^2-5lambda+3)x+10 is a decreasing function for all x in R , find the permissible values of lambdadot