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

Integration Formulas: p. 484 The “Biggies” 𝑢 𝑛 𝑑𝑢 𝑒 𝑢 𝑑𝑢 sin 𝑢 𝑑𝑢 c𝑜𝑠 𝑢 𝑑𝑢 𝑠𝑒𝑐 2 𝑢 𝑑𝑢 𝑑𝑢 𝑢 Inverse trig Inegrals

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

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

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

4) Expand 𝑥+1 2 𝑥 𝑑𝑥

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

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

6. Trig Identities (more in Sec 7.3)

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

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

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

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