" (i) "log[(x^(2)+x+1)/(x^(2)-x+1)]

Prove that, (d)/(dx) ["log" (x^(2) + x + 1)/(x^(2) -x + 1) + (2)/(sqrt3) "tan"^(-1) (sqrt3x)/(1-x^(2))]= (4)/(x^(4 ) + x^(2) + 1)

Differentiate log((x^(2)+x+1)/(x^(2)-x+1)) with respect to x:

Prove that : d/dx[log((x^(2)+x+1)/(x^(2)-x+1))+2/sqrt3tan^(-1)((xsqrt3)/(1-x^(2)))]=4/(1+x^(2)+x^(4))

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

Statement -1 : If I_(1)=int(e^(x))/(e^(4x)+e^(2x)+1)dx and I_(2)=int(e^(-x))/(e^(-4x)+e^(-2x)+1)dx , then I_(2)-I_(1)=(1)/(2)log((e^(2x)-e^(x)+1)/(e^(2x)+e^(x)+1))+C where C is an arbitrary constant. Statement -2 : A primitive of f(x) =(x^(2)-1)/(x^(4)+x^(2)+1) is (1)/(2)log((x^(2)-x+1)/(x^(2)+x+1)) .

Statement -1 : If I_(1)=int(e^(x))/(e^(4x)+e^(2x)+1)dx and I_(2)=int(e^(-x))/(e^(-4x)+e^(-2x)+1)dx , then I_(2)-I_(1)=(1)/(2)log((e^(2x)-e^(x)+1)/(e^(2x)+e^(x)+1))+C where C is an arbitrary constant. Statement -2 : A primitive of f(x) =(x^(2)-1)/(x^(4)+x^(2)+1) is (1)/(2)log((x^(2)-x+1)/(x^(2)+x+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)

Evaluate underset(-1)overset(1)int log((x^2+x+1)/(x^2-x+1))dx .