You actually 𝑐𝑎𝑛 integrate 1/x using the power rule (with a little help from l'Hôpital)pic.twitter.com/tvuQrjFFmC
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You want a list? 1/ Having x both in the bounds and the integrand; 2/ the initial limit/integral exchange; 3/ the denominator being linear, you differentiate rather than use de l'Hôpital ; 4/ n is an integer, I don't like making it real to take the limit; 1/2
1. fair point, but like it or not it's completely clear 2. see thread 3. l'Hôpital says you differentiate both numerator and denominator 4. the power rule is not just true for integers
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1. No it's not, I would remove points on an essay if a students wrote it 2. Yes I know why it is valid, but then put in the video 3. True but as we say in French it's like using a drill to kill a fly 4. True but it's not very pedagogical (pretty sure my undergrads would cry)
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1. I will accept this as valid 2. No, just read a little more 3. "true" is all i needed 4. "true" is all i needed
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If you know enough stuff to know 4, you probably know how to derivate x -> ln(x)
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That's not the point. The point is that it's not that the power rule "doesn't work" for 1/ x, it's that you have to take the limit for it to work
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