Chapter 5: Q. 49 (page 417)
Solve each of the integrals in Exercises 21–70. Some integrals require substitution, and some do not. (Exercise 69 involves a hyperbolic function.)
Short Answer
The solution of the given integral is .
Chapter 5: Q. 49 (page 417)
Solve each of the integrals in Exercises 21–70. Some integrals require substitution, and some do not. (Exercise 69 involves a hyperbolic function.)
The solution of the given integral is .
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Get started for freeComplete 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.
List some things which would suggest that a certain substitution u(x) could be a useful choice. What do you look for when choosing u(x)?
Solve the integral:
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.
Find three integrals in Exercises 27–70 for which either algebra or u-substitution is a better strategy than integration by parts.
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