" 4."(1)/(sqrt(4x^(2)-1))

(1)/(sqrt(1-(4x)^(2)))

(1)/(sqrt(21+4x-x^(2)))

If x+sqrt(x^(2)-1)+(1)/(x+sqrt(x^(2)+1))=20 then x^(2)+sqrt(x^(4)-1)+(1)/(x^(2)+sqrt(x^(4)-1))=

(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(x^4-1)/(x^2sqrt(x^4+x^2+1))dx= sqrt(x^2+1/(x^2)+1)+C (sqrt(x^4+x^2+1))/(x^2)+C (sqrt(x^4+x^2+1))/x+C (d) none of these

int(x^4-1)/(x^2sqrt(x^4+x^2+1))dx= (a) sqrt(x^2+1/(x^2)+1)+C (b) (sqrt(x^4+x^2+1))/(x^2)+C (c) (sqrt(x^4+x^2+1))/x+C (d) none of these

int(x^4-1)/(x^2sqrt(x^4+x^2+1))dx= (a) sqrt(x^2+1/(x^2)+1)+C (b) (sqrt(x^4+x^2+1))/(x^2)+C (c) (sqrt(x^4+x^2+1))/x+C (d) none of these

lim_(xto oo)(sqrt(4x^(2)+2x+1)-sqrt(4x^(2)+1)) is

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