1. Agenda: Feb. 4 HW Check Practice 7.1 Integration overview
Quote of the Day: "After years of finding mathematics easy, I finally reached integral calculus and came up against a barrier. I realized that this was as far as I could go, and to this day I have never successfully gone beyond it in any but the most superficial way." -- Isaac Asimov
Agenda: Feb. 4
HW Check
Practice
7.1 Integration overview

2. Integration Formulas:
p The “Biggies”
𝑢 𝑛 𝑑𝑢
𝑒 𝑢 𝑑𝑢
sin 𝑢 𝑑𝑢
c𝑜𝑠 𝑢 𝑑𝑢
𝑠𝑒𝑐 2 𝑢 𝑑𝑢
𝑑𝑢 𝑢
Inverse trig Inegrals

3. Integration Techniques p. 485
Separate numerator
Complete the square
Add/subtract terms in numerator
Expand
Divide improper rational functions
Trig identities
Multiply/divide Pythagorean conjugate

4. 2𝑥 𝑥 2 +6𝑥+13 𝑑𝑥 Integration tip: try u-sub first Example using:
add/subtract what’s missing ,
separate numerator, complete the square
2𝑥 𝑥 2 +6𝑥+13 𝑑𝑥

5. Example using:
add/subtract what’s missing
Separate numerator
1 1+ 𝑒 𝑥 𝑑𝑥

6. 4) Expand
𝑥 𝑥 𝑑𝑥

7. 5) Divide Improper Rational
𝑥 2 𝑥 2 +1 𝑑𝑥

8. 6. Trig Identities (more in Sec 7.3)
tan 𝑥 𝑑𝑥

9. 6. Trig Identities (more in Sec 7.3)

10. 7. Pythagorean conjugate
1 1+sin⁡(𝑥) 𝑑𝑥

11. Similar but different 2 𝑥 2 +4 𝑑𝑥 2𝑥 𝑥 2 +4 𝑑𝑥 2 𝑥 2 𝑥 2 +4 𝑑𝑥
2 𝑥 2 +4 𝑑𝑥
2𝑥 𝑥 2 +4 𝑑𝑥
2 𝑥 2 𝑥 2 +4 𝑑𝑥
2 𝑥 3 𝑥 2 +4 𝑑𝑥

12. Log Forms and substitution
𝑒 𝑥 1+ 𝑒 𝑥 𝑑𝑥
ln⁡(𝑥) 𝑥 𝑑𝑥
𝑠𝑒𝑐 2 𝑥 tan 𝑥 𝑑𝑥

13. HOMEWORK 19
p. 486 ## 21, 25-33(odd), 39, 43,45, 49, 51, 55, 56, 57, 61, 67, 69
Challenge Problem – due Friday