Solving all the integrals from the 2023 MIT integration bee finals

Sit back, relax and enjoy the wild ride of evaluating the beastly integrals from the 2023 finals. Thank you Myers for the wonderful solution development for problem 2. Thank you Poro :D for the timestamps: Q1 :  0:11  Q2 :  4:49  Q3 :  12:26  Q4 :  21:24