math quiz

MATH 005B Integration Quiz: (60 pts)

Use whatever method you prefer – show all your steps. Try to find the method yourself, rather than just

sticking these into some “integral calculator.”

1. (10 PTS) ∫ 𝑑𝑥

(𝑥2−1) 3 2

3

2 – Give an exact answer.

2. (6 pts) ∫ 𝑥 𝑑𝑥

𝑒 𝑥 5

1 – Give an exact answer!

3. (8 pts) ∫ sin(3𝑥) cos(4𝑥) 𝑑𝑥 – Use integration by parts or the

product-to-sum formula.

4. (6 pts) ∫ sec3(𝑥) tan(𝑥) 𝑑𝑥

5. (10 pts) ∫ 𝑥2

√9−𝑥2 𝑑𝑥

6. (8 pts) ∫ 𝑥+1

𝑥2+4𝑥+5 𝑑𝑥

7. (6 pts) ∫ 𝑥2 𝐿𝑛(𝑥)𝑑𝑥 3

1 – Give an exact answer

8. (6 pts) ∫ 𝑡𝑎𝑛3(𝑥)𝑑𝑥