Question Number 212049 by Spillover last updated on 28/Sep/24
Answered by Ghisom last updated on 28/Sep/24
![∫_0 ^1 (dx/( (√(−ln x))))= [t=(√(−ln x))] =−2∫_∞ ^0 e^(−t^2 ) dt=(√π)](Q212063.png)
$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\frac{{dx}}{\:\sqrt{−\mathrm{ln}\:{x}}}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{−\mathrm{ln}\:{x}}\right] \\ $$$$=−\mathrm{2}\underset{\infty} {\overset{\mathrm{0}} {\int}}\mathrm{e}^{−{t}^{\mathrm{2}} } {dt}=\sqrt{\pi} \\ $$
Commented by Spillover last updated on 28/Sep/24
$${great}.{thanks} \\ $$