log(tan^(-1)x)

If f(x)=int((1-ln(tan^(-1)x))/(1+(ln(tan^(-1)x))^(2)))^(2)(dx)/(1+x^(2)) then f(tan1)-f(tan(1)/(e)) is equal to

Find the derivative of y = log(tan^-1x) .

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

intsin^(-1)((2x)/(1+x^(2)))dx is equal to a) xtan^(-1)x-ln|sec(tan^(-1)x)|+C b) xtan^(-1)x+ln|sec(tan^(-1)x)|+C c) xtan^(-1)x-ln|cos(tan^(-1)x)|+C d)None of these

Prove that ln(1+x)>(tan^(-1)x)/(1+x),x>0

If f(x)=ln(1+x)-(tan^(-1)x)/(1+x) , (for x> 0) then sgn f(x) is ( sgn represents signum function)

If g(x)=ln(1+x)(tan^(-1)x)/(1+x),xgt0 then sgn(g(x)) is,(where sgn(.) represents signum function)

int e^(log(1+tan^(2)x))dx=

int e^(log(1+tan^(2)x))dx=