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Question Number 90024 by Rio Michael last updated on 20/Apr/20

$${\sinh }^{-1}\left[\ln (x+\sqrt{x^2+1})\right]=?$$

Commented by Rio Michael last updated on 21/Apr/20

$$\mathrm{really}\mathrm{sir},$$$$\mathrm{how}\mathrm{about}\underset{x\to 0}{\lim }\sinh (\ln (x+\sqrt{x^2+1})$$

Commented by MJS last updated on 21/Apr/20

$$\sinh \left(\ln (x+\sqrt{x^2+1})\right)=x$$$$\Rightarrow \ln (x+\sqrt{x^2+1})={\sinh }^{-1}x$$$${\sinh }^{-1}\left({\sinh }^{-1}x\right)\mathrm{cannot}\mathrm{be}\mathrm{simplified}$$

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