`sqrt(x+isqrt(x^4+x^(2)+1))=+-(1)/(sqrt(2))[sqrt(x^(2)+x+1)+isqrt (x^2-x+1)]`

lim_(x rarr1)(sqrt(x^(2)-1)+sqrt(x-1))/(sqrt(x^(2)-1))

sqrt(x^(2)+x+4)+sqrt(x^(2)+x+1)=sqrt(2x^(2)+2x+4)

int(sqrt(1-x^(2))-x)/(sqrt(1-x^(2))(1+xsqrt(1-x^(2))))dx is

Simplify (x+sqrt(x^(2)-1))/(x-sqrt(x^(2)-1))+(x-sqrt(x^(2)-1))/(x+sqrt(x^(2)-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(sqrt(1-x^(2))+sqrt(1+x^(2)))/(sqrt(1-x^(2))sqrt(1+x^(2)))dx=

IfI=int(dx)/(x^(3)sqrt(x^(2)-1)), then Iequals a.(1)/(2)((sqrt(x^(2)-1))/(x^(3))+tan^(-1)sqrt(x^(2)-1))+C b.(1)/(2)((sqrt(x^(2)-1))/(x^(2))+x tan^(-1)sqrt(x^(2)-1))+Cc(1)/(2)((sqrt(x^(2)-1))/(x^(2))+tan^(-1)sqrt(x^(2)-1))+Cd(1)/(2)((sqrt(x^(2)-1))/(x^(2))+tan^(-1)sqrt(x^(2)-1))+C

Differentiate (sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2)))wr,rtsqrt(1-x^(4))

Differentiate (sqrt(x^(2)+1)+sqrt(x^(2)-1))/(sqrt(x^(2)+1)-sqrt(x^(2)-1)) with respect to x: