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# AP Calculus BC Integration By Parts

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Integration by Parts

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### AP Calculus BC Integration By Parts

1. 1. AP Calculus BC Integration by Parts
2. 2. 𝑢 𝑑𝑣 = 𝑢𝑣 − 𝑣 𝑑𝑢 Integration by Parts Part I Deriving the Form With polynomial, trigonometric, and transcendental functions With indefinite and definite integrals
3. 3. Examples 1. Find 𝑥𝑒 𝑥 𝑑𝑥 - basic examples 2. Find 𝑥2 ln 𝑥 𝑑𝑥 - basic examples 3. Find sin−1 𝑥 𝑑𝑥 - inverse trigonometric functions 4. Find ln 𝑥 𝑑𝑥 - logarithmic functions 5. Find 𝑥2 sin 𝑥 𝑑𝑥 - repeated integration 6. Find 𝑥2 sin 4𝑥 𝑑𝑥 - tabular integration 7. Find 𝑒2𝑥 sin 𝑥 𝑑𝑥 - solving for the unknown integral 8. Find 0 𝜋/2 𝑥 cos 𝑥 𝑑𝑥 - with definite integrals
4. 4. Video: Integration By Parts - Deriving the Formula
5. 5. Video: Integration By Parts - Basic Examples - Part 1
6. 6. Video: Integration By Parts - Basic Examples - Part 2
7. 7. Video: Integration By Parts - Inverse Trig Functions
8. 8. Video: Integration By Parts - Logarithmic Functions
9. 9. Video: Integration By Parts - Repeated Integration
10. 10. Video: Integration By Parts - Tabular Integration
11. 11. Video: Integration By Parts - Solving for the Unknown Integral - Part I Video: Integration By Parts - Solving for the Unknown Integral - Part II
12. 12. Video: Integration By Parts - Definite Integrals