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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] nikolaj |
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| $\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) $ | ||
| - | The function $\frac{x}{x-1}\log(x)$ is one without bad behaviours (singularities) on $[0,\infty)$. | + | <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 $[0,\infty)$. | ||
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