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## Article 19Logarithmic Expression of Anti-Functions.

Let

Prob. 46.
Show from (38), (39), that, when $x\doteq \infty$,
 ${sinh}^{-1}x-logx\doteq log2,\phantom{\rule{2em}{0ex}}{cosh}^{-1}x-logx\doteq log2,$

and hence show that the integration-constants in (32), (33) are each equal to $log2$.

Prob. 47.
Derive from (42) the series for ${tanh}^{-1}x$ given in (34).
Prob. 48.
Prove the identities:

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