The solution of $$ \int \frac{1}{\sqrt{x^{2} \pm a^{2}}}\, \operatorname{d}x $$ is $\ln\left( x+ \sqrt{x^{2} \pm a^{2}} \right)$. Can this be represented in hyperbolic form as $\sinh^{-1}\left( \frac{x}{a} \right)$ and $-\cosh^{-1}\left( -\frac{x}{a} \right)$ respectively for positive and negative?
2026-03-27 14:50:29.1774623029
Solution of integrals as Hyperbolic functions
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