Question

Can someone tell my whether this result are correct or not?

Answer 1

\[\int\limits_{1}^{2}\frac{ dx }{ \sqrt{x^2-1} }=acosh(2)\]

Answer 2

\[\lim_{n \rightarrow 1^+}\int\limits_{1}^{2}\frac{ dx }{ \sqrt{x^2-1} }=\lim_{n \rightarrow 1^+}\left[ acosh \right]^{2}_{n}=\lim_{n \rightarrow 1^+}acosh(2)-acosh(n)=acosh(2)\]

Answer 3

how can you get it?

Answer 4

Let \[f(x)=\frac{ 1 }{ \sqrt{x^2-1} }\]
then
\[f'(x)=acosh(x)\]