MIT Integration Bee 2022 Qualifications Part 1

#mathematics #olympiad #math
The MIT Integration Bee is a yearly tradition during MIT's Independent Activities Period every January run by MIT Math graduate students. The Bee is open to all MIT students, although most who participate are undergraduates.
The qualifier test consists of 20 questions. The top 16 students from the qualifier test take part in the bee. The first round of the bee is a "regular season" with four students competing to solve each integral. Based on regular season performance, 8 students advance to a seeded single-elimination playoff bracket. In the playoffs, pairs of students go head-to-head to determine the Grand Integrator!

[dedekindcuts]

Tried a new type of video. Let me know if you like it and whether I should do part 2!

[morischacter]

for problem 10 it is also a product rule situation, both methods work!