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Author: Tinku Tara

x-x-2-1-3-2-arctan-x-dx-

Question Number 84809 by M±th+et£s last updated on 16/Mar/20 $$\int\frac{{x}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} {arctan}\left({x}\right)}\:{dx} \\ $$ Commented by abdomathmax last updated on 18/Mar/20 $${A}\:=\int\:\:\:\:\frac{{x}}{\left({x}^{\mathrm{2}\:} +\mathrm{1}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} \:{arctanx}}\:{changement}\:{arctanx}={t} \\…

lim-x-pi-2-cos-2-x-2-2-1-cos-x-x-pi-3-

Question Number 19271 by Joel577 last updated on 08/Aug/17 $$\underset{{x}\rightarrow\pi} {\mathrm{lim}}\:\left(\mathrm{2}\:−\:\mathrm{cos}^{\mathrm{2}} \:{x}\right)^{\frac{\mathrm{2}\sqrt{\mathrm{2}\left(\mathrm{1}\:+\:\mathrm{cos}\:{x}\right)}}{\left({x}\:−\:\pi\right)^{\mathrm{3}} }} \\ $$ Answered by ajfour last updated on 09/Aug/17 $$=\underset{{x}\rightarrow\pi} {\mathrm{lim}}\left\{\left[\mathrm{1}+\mathrm{sin}\:^{\mathrm{2}} \left(\pi−\mathrm{x}\right)\right]^{\frac{\mathrm{1}}{\mathrm{sin}\:^{\mathrm{2}}…

Question-19268

Question Number 19268 by khamizan833@yahoo.com last updated on 08/Aug/17 Answered by ajfour last updated on 08/Aug/17 $$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}\left(\frac{\mathrm{1}}{\mathrm{1}−\mathrm{2}^{\mathrm{x}} }−\frac{\mathrm{1}}{\mathrm{2}}\right) \\ $$$$\mathrm{f}\left(\mathrm{x}\right)+\mathrm{f}\left(−\mathrm{x}\right)=\mathrm{x}\left[\left(\frac{\mathrm{1}}{\mathrm{1}−\mathrm{2}^{\mathrm{x}} }−\frac{\mathrm{1}}{\mathrm{2}}\right)−\left(\frac{\mathrm{2}^{\mathrm{x}} }{\mathrm{2}^{\mathrm{x}} −\mathrm{1}}−\frac{\mathrm{1}}{\mathrm{2}}\right)\right] \\ $$$$\:\:\:\:\:\:\:\:\:\:\:=−\frac{\left(\mathrm{2}^{\mathrm{x}}…

Question-19264

Question Number 19264 by mondodotto@gmail.com last updated on 08/Aug/17 Commented by Satyamtt last updated on 08/Aug/17 $$\mathrm{Is}\:\mathrm{it}\:\mathrm{23}\:?\:\left(\mathrm{by}\:\mathrm{method}\:\mathrm{of}\:\mathrm{differences}\right) \\ $$ Commented by RasheedSindhi last updated on…

ultimately-Q-149894-boils-down-to-finding-s-max-s-min-h-scos-pi-6-2-k-ssin-pi-6-2-r-2-

Question Number 150331 by ajfour last updated on 11/Aug/21 $${ultimately}\:\:{Q}.\mathrm{149894}\:\:{boils}\: \\ $$$${down}\:{to}\:{finding}\:{s}_{{max}} ,\:{s}_{{min}} \:\forall \\ $$$$\:\:\:\:\left\{{h}−{s}\mathrm{cos}\:\left(\theta−\frac{\pi}{\mathrm{6}}\right)\right\}^{\mathrm{2}} \\ $$$$+\left\{{k}−{s}\mathrm{sin}\:\left(\theta+\frac{\pi}{\mathrm{6}}\right)\right\}^{\mathrm{2}} ={r}^{\mathrm{2}} \\ $$$$ \\ $$ Terms of…