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Evaluate the following indefinite integral as a power series:

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

Help appreciated!

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  • $\begingroup$ Where are you running into problems? Is it in the conversion to power series, or is it in the integration of the series? (That changes the question entirely) $\endgroup$ – apnorton Apr 8 '13 at 1:48
  • $\begingroup$ integrating it as a power series $\endgroup$ – user67253 Apr 8 '13 at 1:56
  • $\begingroup$ This integral is called dilogarithm $\endgroup$ – Hanul Jeon Apr 8 '13 at 3:00
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$$\log{(1-t)} = -\sum_{n=1}^{\infty} \frac{t^n}{n}$$

$$\int dt \frac{\log{(1-t)}}{t} = -\sum_{n=1}^{\infty} \frac{t^n}{n^2}$$

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