" 3."(x^(2)tan^(-1)x)/(1+x^(2))

[ If xgt0 then which of the following is true 1) tan^(-1)xgt(x)/(1+x^(2)), 2) tan^(-1)x=(x)/(1+x^(2)) 3) tan^(-1)xlt(x)/(1+x^(2)), 4) tan^(-1)x!=(x)/(1+x^(2))]

Prove that tan^(-1)x+tan^(-1)((2x)/(1-x^(2)))=tan^(-1)((3x-x^(3))/(1-3x^(2)))|x|lt1/(sqrt(3))

Prove the following: tan^(-1)x+tan^(-1)((2x)/(1-x^(2)))=tan^(-1)((3x-x^(3))/(1-3x^(2)))

Let tan^(-1)y=tan^(-1)x+tan^(-1)((2x)/(1-x^(2))) where |x|<(1)/(sqrt(3))* Then a value of y is : (1)(3x-x^(3))/(1-3x^(2))(2)(3x+x^(3))/(1-3x^(2))(3)(3x-x^(3))/(1+3x^(2))(4)(3x+x^(3))/(1+3x^(2))

Prove that tan^(-1) ((3x-x^(3))/(1-3x^(2)))=tan^(-1)x +"tan"^(-1)(2x)/(1-x^(2)), |x| lt (1)/(sqrt(3)) .

For real numbers alpha, beta, gamma and delta , if int((x^(2)-1)+tan^(-1)((x^(2)+1)/(x)))/((x^(4)+3x^(2)+1)tan^(-1)((x^(2)+1)/(x)))dx = alpha log_(e)(tan^(-1)((x^(2)+1)/(x)))+beta "tan"^(-1)((gamma(x^(2)-1))/(x))+delta tan ((x^(2)+1)/(x))+C where is an arbitrary constant, then the value of 10(alpha+betagamma+delta) is equal to........

show that tan^(-1)x+tan^(-1)((2x)/(1-x^2))=tan^(-1)((3x-x^3)/(1-3x^2)),|x|<1/sqrt3

show that tan^(-1)x+tan^(-1)((2x)/(1-x^2))=tan^(-1)((3x-x^3)/(1-3x^2)),|x|<1/sqrt3