(log sec^(-1)x)/(x sqrt(x^(2)-1))

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

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

int(sqrt(x-1))/(x sqrt(x+1))dxquad is equal to ln|x-sqrt(x^(2)-1)|-tan^(-1)x+cln|x+sqrt(x^(2)-1)|-tan^(-1)x+cln|x-sqrt(x^(2)-1)|-sec^(-1)x+cln|x+sqrt(x^(2)-1)|-sec^(-1)x+c

The domain of f(x)=(log(sin^(-1)sqrt(x^(2)+x+1)))/(log(x^(2)-x+1)) is

The domain of f(x)=(log(sin^(-1)sqrt(x^(2)+x+1)))/(log(x^(2)-x+1)) is

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

STATEMENT-1: lim_(x rarr oo)(log[x])/(sqrt(([x])/(sec^(2)-1)))=0 STATEMENT-2: lim_(x rarr0)(sqrt(sec^(2)-1))/(x) does not exist.STATEMENT-3: lim_(x rarr2)(x-1)^((1)/(x-2))=1

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))

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

int(sqrt(x-1))/(xsqrt(x+1))dxi se q u a lto ln|x-sqrt(x^2-1)|-tan^(-1)x+c ln|x+sqrt(x^2-1)|-tan^(-1)x+c ln|x-sqrt(x^2-1)|-sec^(-1)x+c ln|x+sqrt(x^2-1)|-sec^(-1)x+c