Chapter 7 - Exponential Functions - 7.9 Hyperbolic Functions - Exercises - Page 384: 58

$$ \sinh^{-1}(1)$$

Since $$\frac{d}{dx}\sinh^{-1}x=\frac{1}{\sqrt{1+x^2}}$$ Then \begin{align*} \int_{0}^{1} \frac{1}{\sqrt{1+x^{2}}} d x&= \sinh^{-1}x\bigg|_{0}^{1}\\ &= \sinh^{-1}(1)- \sinh^{-1}(0)\\ &= \sinh^{-1}(1) \end{align*}