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natural_logarithm_of_real_numbers [2016/08/14 14:37] nikolaj |
natural_logarithm_of_real_numbers [2016/09/09 08:28] nikolaj |
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| - | $\int_0^y \frac {1 } {1+x } {\mathrm d}x = \ln(1+y) $ | + | |
| + | $\int_1^y \frac {1 } {x} {\mathrm d}x = \ln(y) $ | ||
| + | |||
| + | $\int_0^{y} \frac {1 } {1+x } {\mathrm d}x = \ln(1+y) $ | ||
| + | |||
| + | The function | ||
| + | |||
| + | $\dfrac{x}{x-1}\log(x)$ is one without bad behaviours (singularities) on $[0,\infty)$. | ||
| ----- | ----- | ||
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| === Subset of === | === Subset of === | ||
| [[Real logarithm]], [[Natural logarithm of complex numbers]] | [[Real logarithm]], [[Natural logarithm of complex numbers]] | ||
| === Context === | === Context === | ||
| [[Exponential function]], [[Inverse function]] | [[Exponential function]], [[Inverse function]] | ||
