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Author: Tinku Tara

Question-210127

Question Number 210127 by essaad last updated on 31/Jul/24 Answered by lepuissantcedricjunior last updated on 01/Aug/24 $$\int_{\mathrm{1}} ^{\mathrm{2}} \frac{\boldsymbol{{ln}}\left(\mathrm{1}+\boldsymbol{{x}}\right)−\boldsymbol{{lnx}}}{\boldsymbol{{x}}^{\mathrm{2}} }\boldsymbol{{dx}}=\int_{\mathrm{1}} ^{\mathrm{2}} \frac{\boldsymbol{{ln}}\left(\mathrm{1}+\boldsymbol{{x}}\right)}{\boldsymbol{{x}}^{\mathrm{2}} }\boldsymbol{{dx}}−\int_{\mathrm{0}} ^{\mathrm{2}} \frac{\boldsymbol{{lnx}}}{\boldsymbol{{x}}^{\mathrm{2}}…

show-that-0-1-lnx-x-2-1-dx-2-8-

Question Number 210098 by klipto last updated on 30/Jul/24 $$\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{lnx}}}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{1}}\boldsymbol{\mathrm{dx}}=\frac{\boldsymbol{\pi}^{\mathrm{2}} }{\mathrm{8}} \\ $$ Commented by AlagaIbile last updated on 30/Jul/24…

1-1-2003-1-2004-1-2005-1-2006-1-2007-1-2008-1-2009-Help-me-

Question Number 210085 by Ismoiljon_008 last updated on 30/Jul/24 $$ \\ $$$$\:\:\frac{\mathrm{1}}{\frac{\mathrm{1}}{\mathrm{2003}}+\frac{\mathrm{1}}{\mathrm{2004}}+\frac{\mathrm{1}}{\mathrm{2005}}+\frac{\mathrm{1}}{\mathrm{2006}}+\frac{\mathrm{1}}{\mathrm{2007}}+\frac{\mathrm{1}}{\mathrm{2008}}+\frac{\mathrm{1}}{\mathrm{2009}}}\:=\:? \\ $$$$\:\:\:\mathscr{H}{elp}\:{me} \\ $$$$ \\ $$ Answered by Frix last updated on 30/Jul/24…