Differences

This shows you the differences between two versions of the page.

Link to this comparison view

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] (current)
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 $[0,​\infty)$.
Link to graph
Log In
Improvements of the human condition