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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Replying to @InertialObservr
Dude what you're calling de l'Hôpital rule is just the definition of a derivative...
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Replying to @tomrzah @InertialObservr
Il utilise bien la règle de l'Hôpital pour la limite du terme de droite.
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Replying to @HydrePrever @InertialObservr
J'ai du mal à le voir... Et y'a tellement de choses qui me gênent dans sa vidéo, comme avoir x dans les bornes et l'intégrande de son intégrale...
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Replying to @InertialObservr @HydrePrever
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
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Replying to @tomrzah @HydrePrever
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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Replying to @InertialObservr @tomrzah
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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Replying to @InertialObservr @tomrzah
That could be the point if we decide that this vid is not for giggles but that it could seriously be a way to prove that the primitive of x -> 1/x is x -> ln(x). Is it realist to prove all is needed for this to work in rigorous manner *before* talking seriously about ln?
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