Homework 5 Solution - Integration by Substitution SUGGESTED REFERENCE MATERIAL As you work through the problems listed below you should reference

Homework 5 Solution - Integration by Substitution SUGGESTED...

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Integration by Substitution SUGGESTED REFERENCE MATERIAL: As you work through the problems listed below, you should reference Chapter 5.3 of the rec- ommended textbook (or the equivalent chapter in your alternative textbook/online resource) and your lecture notes. EXPECTED SKILLS: Know how to simplify a “complicated integral” to a known form by making an appro- priate substitution of variables. PRACTICE PROBLEMS: For problems 1-21, evaluate the given indefinite integral and verify that your answer is correct by differentiation. 1. Z 3 x 2 ( x 3 + 3) 3 dx 1 4 ( x 3 + 3) 4 + C 2. Z 5 5 x + 3 dx ln | 5 x + 3 | + C 3. Z 2 x cos ( x 2 ) dx sin ( x 2 ) + C 4. Z 4 x ( x 2 + 6) 2 dx 2 3 ( x 2 + 6) 3 + C 5. Z sec (4 x ) tan (4 x ) dx 1 4 sec (4 x ) + C 6. Z (3 x - 5) 9 dx 1 30 (3 x - 5) 10 + C 1
2
15.dx(HINT: Complete the square) Z 1

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