Question Number 222224 by MrGaster last updated on 20/Jun/25
$$\mathrm{Prove}:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}\left(\mathrm{1}−{x}^{\mathrm{2}} \right)}{{x}}\mathrm{cos}\left(\mathrm{ln}\:{x}\right){dx}=\mathrm{1}−\frac{\pi}{\mathrm{2}}\mathrm{cosh}\frac{\pi}{\mathrm{2}} \\ $$
Commented by Nicholas666 last updated on 21/Jun/25
$$\:\mathrm{i}\:\mathrm{think}\:\mathrm{the}\:\mathrm{statment}\:\mathrm{is}\:\mathrm{wrong},\: \\ $$$$\mathrm{no}\:\mathrm{1}−\frac{\pi}{\mathrm{2}}\:\mathrm{cosh}\:\frac{\pi}{\mathrm{2}}\:\mathrm{but}\:\mathrm{1}\:−\frac{\pi}{\mathrm{2}}\mathrm{chot}\:\left(\frac{\pi}{\mathrm{2}}\right) \\ $$