Chapter 5: Q 39. (page 452)
Solve the following integral.
Short Answer
Answer is
Chapter 5: Q 39. (page 452)
Solve the following integral.
Answer is
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Solve the integral:
Find three integrals in Exercises 39–74 that can be solved without using trigonometric substitution.
True/False: Determinewhethereachofthestatementsthat follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.
(a) True or False: is a proper rational function.
(b) True or False: Every improper rational function can be expressed as the sum of a polynomial and a proper rational function.
(c) True or False: After polynomial long division of p(x) by q(x), the remainder r(x) has a degree strictly less than the degree of q(x).
(d) True or False: Polynomial long division can be used to divide two polynomials of the same degree.
(e) True or False: If a rational function is improper, then polynomial long division must be applied before using the method of partial fractions.
(f) True or False: The partial-fraction decomposition of is of the form
(g) True or False: The partial-fraction decomposition of is of the form .
(h) True or False: Every quadratic function can be written in the form
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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