Question Number 200474 by Rupesh123 last updated on 19/Nov/23
Answered by witcher3 last updated on 19/Nov/23
$$\mathrm{erf}\left(\mathrm{x}\right)=\frac{\mathrm{2}}{\:\sqrt{\pi}}\int_{\mathrm{0}} ^{\mathrm{x}} \mathrm{e}^{−\mathrm{t}^{\mathrm{2}} } \mathrm{dt} \\ $$$$\mathrm{ln}\left(\mathrm{x}+\mathrm{ln}\left(\mathrm{x}\right)\right)=\int_{\mathrm{0}} ^{\mathrm{5}} \mathrm{e}^{−\mathrm{t}^{\mathrm{2}} } =\frac{\sqrt{\pi}}{\mathrm{2}}\mathrm{erf}\left(\mathrm{5}\right) \\ $$$$\mathrm{x}+\mathrm{ln}\left(\mathrm{x}\right)=\mathrm{ln}\left(\mathrm{xe}^{\mathrm{x}} \right)=\frac{\sqrt{\pi}}{\mathrm{2}}\mathrm{erf}\left(\mathrm{5}\right) \\ $$$$\mathrm{xe}^{\mathrm{x}} =\mathrm{e}^{\frac{\sqrt{\pi}}{\mathrm{2}}\mathrm{erf}\left(\mathrm{5}\right)} \\ $$$$\mathrm{x}=\mathrm{W}\left(\mathrm{e}^{\frac{\sqrt{\pi}}{\mathrm{2}}\mathrm{erf}\left(\mathrm{5}\right)} \right) \\ $$$$ \\ $$
Commented by Rupesh123 last updated on 20/Nov/23
Very elegant!