1. Natural Base Integration
Section 5.4
Calculus AP/Dual, Revised ©2017
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§5.4: Natural Base Integration

2. §5.4: Natural Base Integration
Guess The Rule
𝒆 𝟐𝒙 𝒅𝒙
2) 𝒆 𝟏 𝟒 𝒙 𝒅𝒙
3) 𝒙 𝒆 𝒙 𝟐 𝒅𝒙
4) 𝐜𝐨𝐬𝒙 𝒆 𝐬𝐢𝐧𝒙 𝒅𝒙
5) 𝒆 𝟏/𝒙 𝒙 𝟐 𝒅𝒙
6) 𝒆 𝒖 𝒅𝒖
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§5.4: Natural Base Integration

3. Antiderivatives of Natural Base
𝒆 𝒖 𝒅𝒖= 𝒆 𝒖 +𝑪
Use 𝒖-substitution to solve
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§5.4: Natural Base Integration

4. §5.4: Natural Base Integration
Example 1
Solve 𝒆 𝟑𝒙+𝟏 𝒅𝒙
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§5.4: Natural Base Integration

5. §5.4: Natural Base Integration
Example 2
Solve 𝟓𝒙𝒆 − 𝒙 𝟐 𝒅𝒙
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§5.4: Natural Base Integration

6. §5.4: Natural Base Integration
Your Turn
Solve 𝒙 𝟐 𝒆 𝒙 𝟑 𝟐 𝒅𝒙
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§5.4: Natural Base Integration

7. §5.4: Natural Base Integration
Example 3
Solve 𝒆 𝟐𝒙 𝟏+ 𝒆 𝟐𝒙 𝒅𝒙
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§5.4: Natural Base Integration

8. §5.4: Natural Base Integration
Example 4
Solve 𝐬𝐢𝐧 𝒙 𝒆 𝐜𝐨𝐬 𝒙 𝒅𝒙
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§5.4: Natural Base Integration

9. §5.4: Natural Base Integration
Example 5
Solve 𝟐 𝒆 𝒙 −𝟐 𝒆 −𝒙 𝒆 𝒙 + 𝒆 −𝒙 𝟐 𝒅𝒙
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§5.4: Natural Base Integration

10. §5.4: Natural Base Integration
Example 6
Solve −𝟐 𝟎 𝒙 𝟐 𝒆 𝒙 𝟑 𝒅𝒙
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§5.4: Natural Base Integration

11. §5.4: Natural Base Integration
Example 6
Solve −𝟐 𝟎 𝒙 𝟐 𝒆 𝒙 𝟑 𝒅𝒙
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§5.4: Natural Base Integration

12. §5.4: Natural Base Integration
Your Turn
Solve 𝟑 𝟒 𝒆 𝟑−𝒙 𝒅𝒙
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§5.4: Natural Base Integration

13. AP Multiple Choice Practice Question 1 (non-calculator)
Solve 𝒙 𝟐 𝒆 𝒙 𝟑 𝒅𝒙 (A) − 𝟏 𝟑 𝐥𝐧 𝒆 𝒙 𝟑 + 𝑪 (B) − 𝒆 𝒙 𝟑 𝟑 + 𝑪 (C) − 𝟏 𝟑 𝒆 𝒙 𝟑 + 𝑪 (D) 𝟏 𝟑 𝐥𝐧 𝒆 𝒙 𝟑 + 𝑪
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§5.4: Natural Base Integration

14. AP Multiple Choice Practice Question 1 (non-calculator)
Solve 𝒙 𝟐 𝒆 𝒙 𝟑 𝒅𝒙
Vocabulary
Connections and Process
Answer and Justifications
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§5.4: Natural Base Integration

15. §5.4: Natural Base Integration
Assignment
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odd
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§5.4: Natural Base Integration