[" 18."tanh^(-1)(x)" is "],[[" (a) "ln(x+sqrt(x^(2)+1))],[" (b) "ln(x+sqrt(x^(2)-1))],[" (c) "(1)/(2)ln((1+x)/(1-x))],[" (d) "(1)/(2)ln((x+1)/(x-1))]]

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

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

" 1."(d)/(dx){log(x+sqrt(x^(2)+1))}=

y=sqrt(x^(2)+1)-log((1)/(x)+sqrt(1+(1)/(x^(2)))), find (dy)/(dx)

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

int((x)/(sqrt(1+x^(2)))-1)log(x+sqrt(1+x^(2)))backslash dx

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

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

int x((ln(x+sqrt(1+x^(2))))/(sqrt(1+x^(2))))dx=a sqrt(1+x^(2))ln(x+sqrt(1+x^(2)))+bx

int(ln((x-1)/(x+1)))/(x^2-1)dx is equal to (a) 1/2(ln((x-1)/(x+1)))^2+C (b) 1/2(ln((x+1)/(x-1)))^2+C (c) 1/4(ln((x-1)/(x+1)))^2+C (d) 1/4(ln((x+1)/(x-1)))^2+C