Differences
This shows you the differences between two versions of the page.
Both sides previous revision Previous revision | |||
natural_logarithm_of_real_numbers [2016/09/09 08:28] nikolaj |
natural_logarithm_of_real_numbers [2019/09/03 15:33] nikolaj |
||
---|---|---|---|
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}] | ||
+ | </code> | ||
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 $[0,\infty)$. |