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Integral Formulas

Intro​

Below are (30/147) advanced integral formulas listed in the appendix of the Higher Mathematics (Tongji University). I will Derive each formula step by step. It may seem futile and impractival to memorize all the formulas, but it is a great opportunity to consolidate integration techniques and appreciate heuristics behind them.

Instructions​

Anecdote​

In my AP Physics C Mechanics class, many students were struggling to Derive the terminal velocity of a free-falling object, and the primary reason was that they can't solve the Integral Formula #21. My teacher back then found a really sophisticated way through hyperbolic trigonometry substitution, and everyone was stunned by the complexity, but I came up with a simple algebraic transformation. Then, I decided to Derive those formulas as a way to unveil those "secrets" beyond the general textbook.