([40],[+1],[+4y],[4x])=(2a^(3))/(x^(4)-a^(4))+log sqrt((x-a)/(x+3))

If y=log(x^(2)+sqrt(x^(4)-a^(4)))," then "y_(1)sqrt(x^(4)-a^(4))=

log_(4)(x^(2)-1)-log_(4)(x-1)^(2)=log_(4)sqrt((4-x)^(2))

int(x^(2))/((x^(2)-4)^(3/2))dx=log|x+sqrt(x^(2)-4)|+A+c then A=

int(x^(2))/((x^(2)-4)^(3/2))dx=log|x+sqrt(x^(2)-4)|+A+c then A=

If y=tan^(-1)((a)/(x))+log sqrt((x-a)/(x+a)), Prove that (dy)/(dx)=(2a^(3))/(x^(4)-a^(4))

y=log[a^(4x).((x-5)/(x+4))^((3)/(4))]

If y=log((1-x^(2))/(1+x^(2))), then (dy)/(dx)=(4x^(3))/(1-x^(4))( b) -(4x)/(1-x^(4))( c) (1)/(4-x^(4))(d)-(4x^(3))/(1-x^(4))

y=log[3^(x)((x+1)/(x-5))^(3/4)]

lim_(x->a){[(a^(1/2)+x^(1/2))/(a^(1/4)-x^(1/4)))^(- 1)-(2(a x)^(1/4))/(x^(3/4)-a^(1/4)x^(1/2)+a^(1/2)x^(1/4)-a^(3/4))]^(- 1)-sqrt2^(log_4 a)}^8

lim_(x rarr a){[(a^((1)/(2))+x^((1)/(2)))/(a^((1)/(4))-x^((1)/(4))))^(-1)-(2(ax)^((1)/(4)))/(x^((3)/(4))-a^((1)/(4))x^((1)/(2))+a^((1)/(2))x^((1)/(4))-a^((3)/(4)))]^(-1)-sqrt(2)^(log_(4)a)}^(8)