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Chapter 5: Q. 39 (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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Find three integrals in Exercises 27–70 for which either algebra or u-substitution is a better strategy than integration by parts.
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.
Write as an algebraic function.
Describe two ways in which the long-division algorithm for polynomials is similar to the long-division algorithm for integers and then two ways in which the two algorithms are different.
Examples: Construct examples of the thing(s) described in the following. Try to find examples that are different than any in the reading.
(a) An integral with which we could reasonably apply trigonometric substitution with .
(b) An integral with which we could reasonably apply trigonometric substitution with .
(c) An integral with which we could reasonably apply trigonometric substitution with .
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