1. NAME THE KEYWORD OR THE METHOD

3. Keywords: Life-Saving Principle I and the natural log function

4. Keywords: Inverse tangent function

5. Keywords: Trig substitution leading into the natural log function, or just use the standard formula.

6. Keywords: Trig substitution leading into the natural log function, or just use the standard formula.

7. Keywords: Inverse sine function

8. Keywords: u-substitution. The trig substitution is not necessary, but still will work.

9. Keywords: Long Division and inverse tangent

10. Keywords: Trig substitution Now use Integration by Parts and continue

11. Keywords: Trig substitution Now use Integration by Parts on the remaining integral

12. Keywords: Partial Fractions! This is because the denominator breaks into factors.

13. Keywords: Long division followed by Life- Saving Principle I. Partial Fractions is really not be needed.

14. Keywords: Completing the square, and the inverse tangent.

15. Keywords: Life-Saving Principle I, leading to the natural logarithm. Partial Fractions are not needed!

16. Keywords: Partial Fractions

17. Keywords: Break the integral. Then use Life-Saving Principle I and inverse tangent

18. Keywords: Break the integral. Then use u-substitution (or candidate method) and a trig substitution (or the standard formula with natural log function)

19. Keywords: Use a u-substitution or the candidate function method.

20. Keywords: Use the trig substitution. There is no radical term, but still this substitution really works! Now continue using one of the Double Angle formulas for the cosine

21. Keywords: Use the trig substitution

22. Keywords: Use a u-substitution or the candidate function method. The trig substitution is not necessary.

23. Keywords: Use the trig substitution Now use Integration by parts and continue.......

24. Keywords: Use the trig substitution Now use Integration by parts and continue.......

25. Keywords: Use Partial Fractions. Since the denominator breaks into factors, this method is better than attempting to complete the square.

26. Keywords: Life-Saving Principle I, leading to the natural logarithm function. Partial Fractions are not needed, even if the denominator breaks into factors!

27. Keywords: Partial Fractions are needed!

28. IT IS CRUCIALTO MEMORIZE THE FOLLOWING FIVE FORMULAS....

29. MEMORIZE!

30. LIFE-SAVING PRINCIPLE I