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Chapter 5: Q. 60 (page 418)
Solve each of the integrals in Exercises 21鈥�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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Solve each of the integrals in Exercises 39鈥�74. Some integrals require trigonometric substitution, and some do not. Write your answers as algebraic functions whenever possible.
Solve given integrals by using polynomial long division to rewrite the integrand. This is one way that you can sometimes avoid using trigonometric substitution; moreover, sometimes it works when trigonometric substitution does not apply.
dx
Consider the integral from the reading at the beginning of the section.
(a) Use the inverse trigonometric substitution to solve this integral.
(b) Use the trigonometric substitution to solve the integral.
(c) Compare and contrast the two methods used in parts (a) and (b).
For each function u(x) in Exercises 9鈥�12, write the differential du in terms of the differential dx.
Solve each of the integrals in Exercises 39鈥�74. Some integrals require trigonometric substitution, and some do not. Write your answers as algebraic functions whenever possible.
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