" 40."log(x+sqrt(x^(2)-1))

log(x+sqrt(1+x^(2)))

Differentiate log((x+sqrt(x^(2)-1))/(x-sqrt(x^(2)-1)))

If y = log (x + sqrt(x ^(2) + 1)) then y _(2)(1) =

int_(-1)^(1) log (x+sqrt(x^(2)+1))dx =

Domain of f(x)=log(1-x)+sqrt(x^(2)-1)

The value of int_(-1)^(1) (log(x+sqrt(1+x^(2))))/(x+log(x+sqrt(1+x^(2))))f(x) dx-int_(-1)^(1) (log(x +sqrt(1+x^(2))))/(x+log(x+sqrt(1+x^(2))))f(-x)dx ,

(log(x+sqrt(x^(2)+1)))/(x) is

[" (v) Differentiate "log[(sqrt(1+x^(2))+x)/(sqrt(1+x^(2))-x)]" w.r.t."],[cos(log x)]

If =(x^(2))/(2)+(x sqrt(x^(2)+1))/(2)+log sqrt(x+sqrt(x^(2)+1)) prove that 2y=x(dy)/(dx)+log((dy)/(dx))

If y=(x^(2))/(2)+(x)/(2) sqrt(x^(2)+1)+log sqrt(x+sqrt(x^(2)+1)) , prove that, 2y=x (dy)/(dx)+log((dy)/(dx))