(a) Use the Endpaper Integral Table to evaluate the given...

(a) Use the Endpaper Integral Table to evaluate the given integral. (b) If you have a CAS, use it to evaluate the integral, and then confirm that the result is equivalent to the one that you found in part (a).
$$\int \frac{1}{x^{2} \sqrt{x^{2}-2}} d x$$

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Key Concepts

Integration Using Standard Integral Tables

This concept involves referring to a collection of pre-evaluated integrals, such as the Endpaper Integral Table, to identify and apply a matching formula to simplify the process of integration. It is especially useful when the integrand fits a formula listed in the table, thereby avoiding lengthy manual integration procedures.

Substitution Techniques in Integration

Substitution methods help transform a complicated integrand into a form that is more readily integrable. In problems involving radicals and rational functions, choosing an appropriate substitution can simplify the square root or rational part of the expression, aligning it with a standard integral form.

Computer Algebra Systems (CAS) for Integration

A CAS is a tool that performs symbolic manipulation and integration, often used to verify results obtained by hand. It automates the integration process and serves as a cross-checking mechanism, ensuring the manual calculation aligns with the computed solution.

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