Hi ! I need help for a small integration

[I_love_everyone]

Hi everyone, and thank you for taking the time to read this.

My problem is simple to understand. How can I integrate this fonction ?

[math]f(x) = 1/(1-1/x)[/math]
It seemed pretty simple to me at first, but then I realized that nothing I know seems to work.
Does anyone have a formula / integration technique to use on this ?

I thank everyone who will take the time to write an answer.

 

[topsquark]

Hi everyone, and thank you for taking the time to read this.

My problem is simple to understand. How can I integrate this fonction ?

[math]f(x) = 1/(1-1/x)[/math]
It seemed pretty simple to me at first, but then I realized that nothing I know seems to work.
Does anyone have a formula / integration technique to use on this ?

I thank everyone who will take the time to write an answer.

[imath]\dfrac{1}{1 - \dfrac{1}{x}} = \dfrac{1}{1 - \dfrac{1}{x}} \cdot \dfrac{x}{x} =[/imath]...

-Dan

 

[I_love_everyone]

Hi Dan, thank you so much for answering.

Indeed, I feel a bit stupid about asking this, now that I have seen your simple trick. This shows how much I lack "vision".
Anyway :

[math]f(x)=1/(1-1/x) = x/(x-1) = x-1+1/(x-1) = 1 + 1/(x-1)[/math]
Now we can integrate easily.
Thanks again.

 

[topsquark]

Hi Dan, thank you so much for answering.

Indeed, I feel a bit stupid about asking this, now that I have seen your simple trick. This shows how much I lack "vision".
Anyway :

[math]f(x)=1/(1-1/x) = x/(x-1) = x-1+1/(x-1) = 1 + 1/(x-1)[/math]
Now we can integrate easily.
Thanks again.

The simplest things are often the hardest to see. No worries!

-Dan