# Differences

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 natural_logarithm_of_real_numbers [2016/09/09 08:28]nikolaj natural_logarithm_of_real_numbers [2019/09/03 15:33] (current)nikolaj Both sides previous revision Previous revision 2019/09/03 15:33 nikolaj 2016/09/09 08:28 nikolaj 2016/09/09 08:28 nikolaj 2016/09/09 08:28 nikolaj 2016/08/14 14:37 nikolaj 2016/08/14 14:37 nikolaj 2015/04/15 14:12 nikolaj 2014/03/21 11:11 external edit2014/02/25 21:27 nikolaj 2014/02/25 21:27 nikolaj 2014/02/25 21:26 nikolaj 2014/02/25 21:25 nikolaj 2014/02/25 21:25 nikolaj 2014/02/13 16:13 external edit2013/09/09 09:24 nikolaj 2013/09/08 15:13 nikolaj created 2019/09/03 15:33 nikolaj 2016/09/09 08:28 nikolaj 2016/09/09 08:28 nikolaj 2016/09/09 08:28 nikolaj 2016/08/14 14:37 nikolaj 2016/08/14 14:37 nikolaj 2015/04/15 14:12 nikolaj 2014/03/21 11:11 external edit2014/02/25 21:27 nikolaj 2014/02/25 21:27 nikolaj 2014/02/25 21:26 nikolaj 2014/02/25 21:25 nikolaj 2014/02/25 21:25 nikolaj 2014/02/13 16:13 external edit2013/09/09 09:24 nikolaj 2013/09/08 15:13 nikolaj created Line 9: Line 9: $\int_0^{y} \frac {1 } {1+x } {\mathrm d}x = \ln(1+y)$ $\int_0^{y} \frac {1 } {1+x } {\mathrm d}x = \ln(1+y)$ + + <​code>​ + Log[a] == Log[b] + Integrate[1/​(t+b)-1/​(t+a),​{t,​0,​Infinity}] + ​ The function $x\mapsto\frac{x}{x-1}\log(x)$ is one without bad behaviours (singularities) on $[0,​\infty)$. The function $x\mapsto\frac{x}{x-1}\log(x)$ is one without bad behaviours (singularities) on $[0,​\infty)$.