Menu Close

Author: Tinku Tara

solve-an-equation-ln-x-ln-x-

Question Number 212123 by MrGaster last updated on 02/Oct/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{solve}\:\mathrm{an}\:\mathrm{equation}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\sqrt{\boldsymbol{\mathrm{ln}}\:\boldsymbol{{x}}}=\boldsymbol{\mathrm{ln}}\sqrt{\boldsymbol{{x}}} \\ $$ Answered by Frix last updated on 02/Oct/24 $$\sqrt{\mathrm{ln}\:{x}}=\frac{\mathrm{ln}\:{x}}{\mathrm{2}} \\…

Question-212130

Question Number 212130 by Ismoiljon_008 last updated on 02/Oct/24 $$\:\:\:\: \\ $$ Answered by a.lgnaoui last updated on 03/Oct/24 $$\:\:\:\:\frac{\mathrm{AD}}{\mathrm{BC}}=\mathrm{2},\mathrm{48}\:\left(\mathrm{detail}\:\mathrm{en}\:\mathrm{commentaire}\right) \\ $$ Commented by a.lgnaoui…

Prove-that-ln-13-1-10-13-2-gt-0-without-calculator-

Question Number 212098 by CrispyXYZ last updated on 30/Sep/24 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{ln}\:\frac{\sqrt{\mathrm{13}}−\mathrm{1}}{\mathrm{10}}\:+\:\sqrt{\mathrm{13}}\:−\:\mathrm{2}\:>\mathrm{0} \\ $$$$\mathrm{without}\:\mathrm{calculator}. \\ $$ Answered by MrGaster last updated on 03/Nov/24 $$\mathrm{ln}\left(\sqrt{\mathrm{13}}−\mathrm{1}\right)−\mathrm{ln}\:\mathrm{10}+\sqrt{\mathrm{13}}−\mathrm{2}>\mathrm{0} \\…

Question-212099

Question Number 212099 by vahid last updated on 30/Sep/24 Answered by mehdee7396 last updated on 30/Sep/24 $$\int\frac{\mathrm{1}+{tan}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}}{\mathrm{1}−{tan}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}}{dx}\:\:\:\:\:;\:{let}\:\:\:{tan}\frac{{x}}{\mathrm{2}}={u} \\ $$$$=\int\frac{\mathrm{2}{u}}{\mathrm{1}−{u}^{\mathrm{2}} }{du}={ln}\frac{\mathrm{1}+{u}}{\mathrm{1}−{u}}+{c} \\ $$$$={ln}\left({tan}\left(\frac{\pi}{\mathrm{4}}+\frac{{x}}{\mathrm{2}}\right)\right)+{c}\:\:\checkmark \\…