Final answer:
A trigonometric substitution can be used to simplify the integral of \( \sqrt{2-x^2}/x \), transforming it into a form involving trigonometric functions, for which standard integral formulas exist.
Step-by-step explanation:
To integrate the function \( \sqrt{2-x^2}/x \), no standard formula from a table of integrals directly applies. However, we can approach this problem by recognizing a possible trigonometric substitution that would simplify the integral.
In this case, one might notice that the radical \( \sqrt{2-x^2} \) suggests using a substitution related to the Pythagorean identity, where \( x = \sqrt{2} \sin(\theta) \).
This would transform the radical into \( \sqrt{2-x^2} = \sqrt{2-(\sqrt{2}\sin(\theta))^2} = \sqrt{2} \cos(\theta) \), turning the original integral into a form that involves trigonometric functions, which are more straightforward to integrate.
Therefore, the chosen formula from the table of integrals would likely be the one related to the integration of trigonometric functions, as the substitution method enables transformations to such forms. It is essential to rewrite the integral in terms of \( \theta \) and \( d\theta \) during the substitution process.