Chapter 5: Q. 9 (page 428)
Explain why choosing (and thus choosing dv to be the entire integrand, including dx) is never a good choice for integration by parts.
Hence proved.
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For each function u(x) in Exercises 9–12, write the differential du in terms of the differential dx.
Solve the integralthree ways:
(a) with the substitution followed by back substitution;
(b) with integration by parts, choosing localid="1648814744993"
(c) with the trigonometric substitution x = sec u.
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.
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).
Solvethe following two ways:
(a) with the substitution
(b) with the trigonometric substitution x = 2 tan u.
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