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anonymous
 one year ago
How do you solve this?
Integrate[f'[x]/f[x],{x,a,t}]
anonymous
 one year ago
How do you solve this? Integrate[f'[x]/f[x],{x,a,t}]

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{a}^{t} \frac{f'(x)}{f(x)} dx\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Maybe we try to define a function g[x] such that \[g'[x] = f'(x) f(x)^{1}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then I can g[t] g[a]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0by fundamental theorem

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so then I guess I'm asking.. how would I convert \[f'(x) f(x)^{1}\] into g(x) ? Is there a rule or method for it? I thought maybe reverse chain rule.. but I'm not seeing how it would apply.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh, irish's post hasnt come through yet. I'll refresh...

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.0he had one and now it is gone

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1\(\large g(x) = \frac{d}{dx}(ln(f(x)) = \frac{1}{f(x)} \ f'(x)\) \(G(x) = \int \ g(x) \ dx = \int \ \frac{d}{dx}(ln(f(x)) \ dx\ = ln(f(x))\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Did we use the ln function with reverse chain rule here? ok.. I think I get it..
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