How do you solve this?

Integrate[f'[x]/f[x],{x,a,t}]

Question

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

anonymous · Answer

$$\int\limits_{a}^{t} \frac{f'(x)}{f(x)} dx$$

anonymous · Answer

Maybe we try to define a function g[x] such that 
$$g'[x] = f'(x) f(x)^{-1}$$

anonymous · Answer

then I can g[t] -g[a]

anonymous · Answer

by fundamental theorem

anonymous · Answer

so 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 · Answer

oh, irish's post hasnt come through yet. I'll refresh...

nincompoop · Answer

he had one and now it is gone

irishboy123 · Answer

$\large g(x) = \frac{d}{dx}(ln(f(x)) = \frac{1}{f(x)} \ f'(x)$

$G(x) = \int \ g(x) \ dx = \int \ \frac{d}{dx}(ln(f(x)) \ dx\ = ln(f(x))$

anonymous · Answer

Did we use the ln function with reverse chain rule here?

ok.. I think I get it..

anonymous · Answer

Thnx irish