# Thread: power series representation #2

1. ## power series representation #2

Evaluate the indefinite integral as a series:

$f(x) = \int \frac{ln(1-t)}{t} dt$

Here is what I did:

$= \frac{1}{t} \int ln(1-t) dt$

$\frac{1}{t} \sum^{\infty}_{n=0} (t)^n$

So, what do I do now? Since I differentiated to get $\frac{1}{1-t}$, do I just need to integrate it now and then multiply $\frac{1}{t}$ back in? Did I miss anything ?

2. Originally Posted by mollymcf2009
Evaluate the indefinite integral as a series:

$f(x) = \int \frac{ln(1-t)}{t} dt$

Here is what I did:

$= \frac{1}{t} \int ln(1-t) dt$

$\frac{1}{t} \sum^{\infty}_{n=0} (t)^n$

So, what do I do now? Since I differentiated to get $\frac{1}{1-t}$, do I just need to integrate it now and then multiply $\frac{1}{t}$ back in? Did I miss anything ?
and exactly why would you factor a function of t out of a dt-integral? you can only factor out constants (with respect to the variable of integration) remember?

Hint: you know the power series for the given log function, just write that in. then divide it through by t. then integrate term by term. well, that's not really a hint, that's how to do the problem

by the way, your power series for the log is incorrect, you wrote the power series for 1/(1 - t) ...which is NOT the integral of ln(1 - t), by the way

3. Originally Posted by Jhevon
and exactly why would you factor a function of t out of a dt-integral? you can only factor out constants (with respect to the variable of integration) remember?

Hint: you know the power series for the given log function, just write that in. then divide it through by t. then integrate term by term. well, that's not really a hint, that's how to do the problem

by the way, your power series for the log is incorrect, you wrote the power series for 1/(1 - t) ...which is NOT the integral of ln(1 - t), by the way
Ok, so what I would have for my power series is:
$
\sum^{\infty}_{n=0} \int \frac{(t)^n}{t} dt$
?

Is that what you said for me to do?

4. Originally Posted by mollymcf2009
Ok, so what I would have for my power series is:
$
\sum^{\infty}_{n=0} \int \frac{(t)^n}{t} dt$
?

Is that what you said for me to do?
question: what does the power series for ln(1 - t) look like? did you use that here?