" ane "((x+1)/(x^(2/3)-x^(1/3)+1)-(x-1)/(x-sqrt(x)))^(10)

The term independent of x in expansion of ((x+1)/(x^(2//3)-x^(1//3)+1)-(x-1)/(x-x^(1//2)))^(10) is:

The term independent of x in the expansion of ((x+1)/(x^(2/3)-x^(1/3)+1)-(x-1)/(x-x^(1/2)))^(10) is -

[((x-1)/(x^((2)/(3))+x^((1)/(3))+1))+((x-1)/(x-sqrt(x)))]^(10) constant term is

((x+1)/(x^(2/3)-x^(1/3)+1)-(x-1)/(x+x^(1/2)))^10 find term independent of x

If y=(1)/(3)"log" (x+1)/(sqrt(x^(2)-x+1))+(1)/(sqrt(3))"tan"^(-1)(2x-1)/(sqrt(3)) , show that, (dy)/(dx)=(1)/(x^(3)+1)

If y=log sqrt((x^(2)+x+1)/(x^(2)-x+1))+(1)/(2sqrt(3)){tan^(-1)backslash(2x+1)/(sqrt(3))+tan^(-1)backslash(2x-1)/(sqrt(3))} then prove that (dy)/(dx)=(1)/(x^(4)+x^(2)+1)

If y=log sqrt((x^(2)+x+1)/(x^(2)-x+1))+(1)/(2sqrt(3)){tan^(-1)backslash(2x+1)/(sqrt(3))+tan^(-1)backslash(2x-1)/(sqrt(3))} then prove that (dy)/(dx)=(1)/(x^(4)+x^(2)+1)