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Chapter 5: Q 11. (page 495)
Fill in the blanks to complete each of the following integration formulas.
The obtained result is.
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Find three integrals in Exercises 27–70 for which a good strategy is to apply integration by parts twice.
Solve given definite integral.
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 .
Find three integrals in Exercises 27–70 for which a good strategy is to use integration by parts with and dv the remaining part.
Solve the following two ways:
(a) with the trigonometric substitution x = 3 tan u;
(b) with algebra and the derivative of the arctangent.
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