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Chapter 5: Q 13. (page 451)
Describe strategy for solving the type of integral given.
Use the formula:
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Give an example of an integral for which trigonometric substitution is possible but an easier method is available. Then give an example of an integral that we still don’t know how to solve given the techniques we know at this point.
Why don’t we need to have a square root involved in order to apply trigonometric substitution with the tangent? In other words, why can we use the substitution when we see , even though we can’t use the substitution unless the integrand involves the square root of? (Hint: Think about domains.)
Explain why, if , then . Your explanation should include a discussion of domains and absolute values.
Solve each of the integrals in Exercises 39–74. Some integrals require trigonometric substitution, and some do not. Write your answers as algebraic functions whenever possible.
Solve the integral:
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