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Home  Exponential and Logartihmic Functions Derivatives and Integrals Involving ln x Examples Example 8 |
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Example 8
Find Assume a > 0. We make the trigonometric substitution x = a sec 6, illustrated in Figure 8.7.1.
Figure 8.7.1 Then dx = a tan θ sec θ dθ,
Therefore
The formula
can be derived in a similar way and is left as an exercise. The integrals
can now be evaluated using integration by parts,
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Last Update: 2006-11-16