Chapter 5: Q 44. (page 452)
Find the integral.
Short Answer
Answer is
Chapter 5: Q 44. (page 452)
Find the integral.
Answer is
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Get started for freeFind three integrals in Exercises 21–70 that we can anti-differentiate immediately after algebraic simplification.
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
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.
Why don’t we need to have a square root involved in order to apply trigonometric substitution with the tangent? In other words, why can we use the substitution when we see , even though we can’t use the substitution unless the integrand involves the square root of? (Hint: Think about domains.)
Explain how to use long division to write the improper fraction as the sum of an integer and a proper fraction.
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