(tan(1+log x))/(x)

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 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

f(x)=((2^(x)-1)^(2))/(tan x log(1+x)),x!=0 and f(x)=2log2,x=0 at x=0 is:

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

int(tan(ln x)tan(ln((x)/(2)))tan(ln2))/(x)dx

Evaluate: (i) int tan x sec^(2)x sqrt(1-tan^(2)x)dx (ii) int log x(sin{1+(log x)^(2)})/(x)dx

Prove that (d)/(dx){2x tan^(-1)x-log (1+x^(2))}=2 tan^(-1)x.

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