" (xii) "sqrt(x^(2)+1)-log[(1)/(x)+sqrt(1+(1)/(x^(2)))]

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

Evaluate lim_(x rarr 1) (sqrt(x^(2)-1)+sqrt(x-1))/(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

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

(d)/(dx) {Tan ^(-1)"" (sqrt(1+ x ^(2))+ sqrt(1- x ^(2)))/( sqrt(1+ x ^(2))- sqrt(1- x ^(2)))}=

Simplify : (a) sqrt(y+sqrt(2xy-x^(2))) + sqrt(y-sqrt(2xy-x^(2))) (b) (x+sqrt(x^2-1))/(x-sqrt(x^(2)-1)) -(x-sqrt(x^(2)-1))/(x+sqrt(x^(2)-1))

if y=(sqrt(x^(2)+1)+sqrt(x^(2)-1))/(sqrt(x^(2)+1)-sqrt(x^(2)-1)), then (dy)/(dx) is

Differentiate the following function (sqrt(x^(2)+1)+sqrt(x^(2)-1))/(sqrt(x^(2)+1)-sqrt(x^(2)-1))