Question Number 194818 by sonukgindia last updated on 16/Jul/23
Answered by sniper237 last updated on 16/Jul/23
$$\overset{{x}={u}^{\mathrm{2}} } {=}\int_{\mathrm{0}} ^{\mathrm{1}} \:\sqrt{\mathrm{1}−{u}}\:×\left(\mathrm{2}{lnu}\right)×\left(\mathrm{2}{udu}\right) \\ $$$$=\:\mathrm{4}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{u}^{\mathrm{2}−\mathrm{1}} \left(\mathrm{1}−{u}\right)^{\frac{\mathrm{3}}{\mathrm{2}}−\mathrm{1}} {lnu}\:{du} \\ $$$$=\:\mathrm{4}\:\partial_{{x}} {B}_{\mid\left(\mathrm{2};\frac{\mathrm{3}}{\mathrm{2}}\right)} \\ $$$${special}\:{Euler}\:{funcions}\: \\ $$