If `(3(x^(1/3) - 1/(x^(1/3))))^(1/3) = 2`, then `x^(1/3) + 1/(x^(1/3)) =`

int dx/(x(1+root(3)(x))^2) is equal to : (i) 3log(x^(1/3)/(1+x^(1/3))+1/(1+x^(1/3)))+C (ii) 3log(((1+x^(1/3))/x^(1/3))+1/(1+x^(1/3)))+C (iii) 3log(((1+x^(1/3))/x^(1/3))+1/(1+x^(1/3)))+C (iv) none of these

If (x^(2) + 1)/(x)= 3(1)/(3) and x gt 1 , find x^(3)- (1)/(x^(3))

(b) If (x^(2)+1)/(x)=3(1)/(3) and x>1 ; find x^(3)-(1)/(x^(3))

If y=(x^(2//3)-x^(-1//3))/(x^(2//3)+x^(-1//3))," then "(x+1)^(2)y_(1)=

Simplify : (x^((1)/(3)) - x^(-(1)/(3)))(x^((2)/(3)) +1+x^(-(2)/(3)))

If x+(1)/(x)=3 and x^(2)+(1)/(x^(3))=5 then the value of x^(3)+(1)/(x^(2)) is

int(dx)/(x(1+root(3)(x))^(2)) is equal to :(i)3log((x^((1)/(3)))/(1+x^((1)/(3)))+(1)/(1+x^((1)/(3))))+C( ii) 3log(((1+x^((1)/(3)))/(x^((1)/(3))))+(1)/(1+x^((1)/(3))))+C( iii) 3log(((1+x^((1)/(3)))/(x^((1)/(3))))+(1)/(1+x^((1)/(3))))+C( iv) none of these

((x+1)/(x^(2/3)-x^(1/3)+1)-(x-1)/(x-x^(1/2)))=

Coefficient of the constant term in the expansion of E=(x^(2/3)+4x^(1/3)+4)^(5)((1)/(x^(1/3)-1)+(1)/(x^(2/3)+x^(1/3)+1))