Integral of the Day | 1.22.26 | Looks Simple, Requires Multiple Substitutions

Today’s Integral of the Day (1.22.26) was sent to me by none other than Alan Bromborsky— my favorite retired physicist, mathematician, and loyal subscriber.

In this video, I walk through the integral using two substitutions, following essentially the same approach Alan used in his original solution. While my final answer is written in terms of natural logarithms, Alan’s solution used hyperbolic functions, leading to an equivalent answer written with an inverse hyperbolic expression. Different routes — same mathematics.

👇 Let me know in the comments:
Did you solve this a different way?
Did you spot a shortcut or take an alternative approach?

Update: After recording this, Dr. Gupta showed me a very clever shortcut solution — I’ll be sharing that method soon.

xoxo,
Professor V

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