`4x^(2) - 4x + 1 = ("__________")^(2)`

If log_((3x+4))(4x^(2)+4x+1)+log_((2x+1))(6x^(2)+11x+4)=4 then x is __________.

lim_ (x rarr (1) / (2)) ((8x-3) / (2x-1) - (4x ^ (2) +1) / (4x ^ (2) -1))

If f(x^(2) - 4x + 4) = x^(2) + 1 . Find f(1) if f(1) lt 8 .

If f(x^(2) - 4x + 4) = x^(2) + 1 . Find f(1) if f(1) lt 8 .

int ((x ^ (-6) -64) / (4 + 2x ^ (-1) + x ^ (-2)) * (x ^ (2)) / (4-4x ^ (-1) + x ^ (-2))-(4x ^ (2) (2x + 1)) / (1-2x)) dx

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 x + (1)/(2x) = 4 , then find x^(2) + (1)/(4x^(2)) .

int ((2x-4) ^ ((1) / (6))) / ((2x-4) ^ ((1) / (4)) + (2x-4) ^ ((1) / (2) )) dx

If 2x - (1)/(2x) =4 , find : (i) 4x^(2) + (1)/( 4x^2)