(1)/(4x^(2)-4x+3)

If f(x)=(1)/(x^(2)+4x+4)-(4)/(x^(4)+4x^(3)+4x^(2))+(4)/(x^(3)+2x^(2)) the f (1/2) is equal to

int(1)/(sqrt(4x^(2)-4x+3))dx=

If f(x) {:(=(x^(2)-4x+3)/(x^(2)-1)", ..."x!=1 ),( =2", ..."x=1):} then :

If f(x) = {((x^(2)-4x+3)/(x^(2)-1), ",","for"x != 1),(2, ",", "for"x = 1 ):} , then

underset(x to 1//2)lim {(8x-3)/(2x-1)-(4x^(2)+1)/(4x^(2)-1)}=

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

int((2x+1))/((x^(2)+4x+1)^(3//2))dx= a) (x^(3))/((x^(2)+4x+1)^(1//2))+C b) (x)/((x^(2)+4x+1)^(1//2))+C c) (x^(2))/((x^(2)+4x+1)^(1//2))+C d) (1)/((x^(2)+4x+1)^(1//2))+C

Prove that: 3cos^(-1)x=cos^(-1)(4x^(3)-3x),x in[(1)/(2),1]