[f(x)^(2)dx[log((x^(2)+x+1)/(x^(2)-x+1))+(2)/(sqrt(3))tan^(-1)((x sqrt(3))/(1-x^(2)))],],[=,(4)/(-(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)

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))

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)

If y=log((x^2+x+1)/(x^2-x+1))+2/(sqrt(3))t a n^(-1)((sqrt(3)x)/(1-x^2)),"f i n d"(dy)/(dx)

int_(-(1)/(sqrt(3)))^(-(1)/(sqrt(3)))(x^(4))/(1-x^(4))cos^(-1)((2x)/(1+x^(2)))dx

int_(th x^(2)(x))^( If )((x+2)dx)/((x^(2)+3x+3)sqrt((x+1)))=(2)/(sqrt(3))[tan^(-1)((f(x)+1)/(sqrt(3)))+tan^(-1)((f(x)-1)/(sqrt(3)))]+c

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)

int (1+x^(2))/(1-x^(2)).(dx)/(sqrt(1+x^(4)))=(1)/(sqrt(2))log|(sqrt(1+x^(4))+xsqrt(2))/(1-x^(2))|+c

(d)/(dx)[cos^(-1)(x sqrt(x)-sqrt((1-x)(1-x^(2))))]=(1)/(sqrt(1-x^(2)))-(1)/(2sqrt(x-x^(2)))(-1)/(sqrt(1-x^(2)))-(1)/(2sqrt(x-x^(2)))(1)/(sqrt(1-x^(2)))+(1)/(2sqrt(x-x^(2)))(1)/(sqrt(1-x^(2)))0 b.1/4c.-1/4d none of these

int_(-1/sqrt3)^(-1/sqrt3)(x^4)/(1-x^4)cos^(- 1)((2x)/(1+x^2))dx