FINALLY an Interesting Integral in the 2024 HSC ?!

Today we'll be solving the a very interesting integral question in this year's HSC Math Extension 1 paper. This question falls under the Extension 2 topic of calculus - solving an integral using u substitution.
I will walk you guys through how to break down and understand the question, and steps on how to problem solve this question.
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Feel free to leave requests for any math problems that you guys want to see me solve in the comment section too.