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I have seen Feynman's integral trick coming into use in many questions, but I don't really see a common way to recognize the format for it. Of course when a question comes with an explicit parameter, it's easy to recognize the pattern and follow the steps known to us in the form of Feynman's Trick. So, is there any standard way to quickly recognize the same being in action for any asked question, i.e., how to observe that the question intends us to make use of Feynman's method?

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  • $\begingroup$ I did try to find a relevant thread for the same, but I couldn't come across anything that would give the clarity needed. But, in case I missed a few threads- I will also appreciate if I could be linked to those threads. $\endgroup$
    – Arsenic
    Aug 1, 2022 at 2:19
  • $\begingroup$ For 90% of the encountered cases it's useless. It is usable only in some very few niche questions $\endgroup$ Aug 1, 2022 at 2:21
  • $\begingroup$ Yeah, this helps a lot! Are there more threads like these and, if yes, could you link me to them as well? $\endgroup$
    – Arsenic
    Aug 1, 2022 at 2:28
  • $\begingroup$ I liked this medium article cantorsparadise.com/… $\endgroup$ Aug 1, 2022 at 2:32
  • $\begingroup$ Thanks, I have gone through this and it's a good read! $\endgroup$
    – Arsenic
    Aug 1, 2022 at 2:34

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Unfortunately, there is no easy way to tell if Feynman's Trick is helpful. You just have to be creative.

One trick I found out is that if you see an integral of the form $\int_a^b \frac{f(h(x))}{h(x)g(x)}$, you can let $I(a) = \int_a^b \frac{f(ah(x))}{h(x)g(x)}$ then take the partial derivative with respect to $a$ to get $I'(a) = \int_a^b \frac{f'(ah(x))}{g(x)}$, which could be easier to work with depending on what $f$ and $g$ are.

Sometimes whenever I try to solve a difficult integral, I choose a parameter inside that integral, go on Symbolab, take the partial derivative with respect to that parameter, and rinse and repeat for different possible parameters to see if I can get an easier function to integrate.

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