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# Integration By Parts Tutorial & Example- Calculus 2

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Easy to Follow Integration By Parts Tutorial & Example- Calculus 2

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### Integration By Parts Tutorial & Example- Calculus 2

1. 1. Calculus 2 Notes <ul><li>--Integration By Parts-- </li></ul>
2. 2. Topic Overview <ul><li>Integration By Parts Basic Rules </li></ul><ul><li>When to let u=x n </li></ul><ul><li>When to let dv=x n </li></ul><ul><li>When to let dv=e ax </li></ul><ul><li>Example problem </li></ul>
3. 3. The Basics <ul><li>Memorize Formula: ∫ u dv = uv - ∫ v du </li></ul><ul><li>Note that ∫ u dv is the original question </li></ul><ul><li>dv ➟ should be most complicated part that can still be integrated </li></ul><ul><li>u ➟ derivative should be simpler than u </li></ul>
4. 4. When to Let u = x n <ul><li>∫ x n e ax dx </li></ul><ul><li>∫ x n sin ax dx </li></ul><ul><li>∫ x n cos ax dx </li></ul>
5. 5. When to Let dv = x n dx <ul><li>∫ x n ln x dx </li></ul><ul><li>∫ x n arcsin(ax) dx </li></ul><ul><li>∫ x n arctan(ax) dx </li></ul>
6. 6. When to Let dv = e ax dx <ul><li>∫ e ax sin(bx) dx </li></ul><ul><li>∫ e ax cos(bx) dx </li></ul>
7. 7. Example = ?
8. 8. Example = ? Recall Formula:
9. 9. Example = ? Recall Formula: u
10. 10. Example = ? Recall Formula: u dv
11. 11. Example = ? Recall Formula: u dv
12. 12. Example = ? Recall Formula: u dv ∫ u dv = u v - ∫ v du
13. 13. Example = ? Recall Formula for Substitutions: u dv u v v du ∫ u dv = u v - ∫ v du
14. 14. Example Recall Formula: u v v du ∫ u dv = u v - ∫ v du
15. 15. Example Recall Formula: u v v du ∫ u dv = u v - ∫ v du
16. 16. Example Recall Formula: u v v du ∫ u dv = u v - ∫ v du
17. 17. Example Recall Formula: u v v du ∫ u dv = u v - ∫ v du
18. 18. Example Recall Formula: u v v du ∫ u dv = u v - ∫ v du Final Answer:
19. 19. That’s all folks! <ul><li>EmpoweringMinds wishes all the best to you in your mathematical endeavors! “Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.” -- Albert Einstein </li></ul>