Chapter 5: Q. 48 (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.)
Short Answer
The solution of the given integral is .
Chapter 5: Q. 48 (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 .
All the tools & learning materials you need for study success - in one app.
Get started for freeFind three integrals in Exercises 27–70 for which either algebra or u-substitution is a better strategy than integration by parts.
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 .
Show by differentiating (and then using algebra) that and are both antiderivatives of . How can these two very different-looking functions be an antiderivative of the same function?
Complete the square for each quadratic in Exercises 28–33. Then describe the trigonometric substitution that would be appropriate if you were solving an integral that involved that quadratic.
Solve the integral:
What do you think about this solution?
We value your feedback to improve our textbook solutions.