Chapter 5: Q. 3 (page 441)
What is a rational function? What does it mean for a rational function to be proper? Improper?
The function that can be expressed as a quotient of polyomial.
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Find three integrals in Exercises 21–70 in which the denominator of the integrand is a good choice for a substitution u(x).
Complete the square for each quadratic in Exercises 28–33. Then describe the trigonometric substitution that would be appropriate if you were solving an integral that involved that quadratic.
For each integral in Exercises 5–8, write down three integrals that will have that form after a substitution of variables.
Find three integrals in Exercises 27–70 for which a good strategy is to use integration by parts with and dv the remaining part.
Explain why, if , then . Your explanation should include a discussion of domains and absolute values.
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