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Question-72346

Question Number 72346 by aliesam last updated on 27/Oct/19 Commented by mathmax by abdo last updated on 27/Oct/19 $${I}\:=\int_{\mathrm{0}} ^{\infty} \:\frac{{ln}\left({x}^{\mathrm{10}} +{x}^{\mathrm{6}} \:+{x}^{\mathrm{4}} \:+\mathrm{1}\right)}{\left({x}+\mathrm{1}\right)^{\mathrm{3}} }{dx}\:\:\:{by}\:{psrts}\:{u}^{'}…

Up-to-which-prime-number-should-9-divide-9631-to-ensure-that-this-number-is-a-prime-number-or-a-composite-number-

Question Number 6810 by Tawakalitu. last updated on 28/Jul/16 $${Up}\:{to}\:{which}\:{prime}\:{number}\:{should}\:\:\:\mathrm{9}\:\:\:{divide}\:\:\:\mathrm{9631}\:\:\:{to}\:{ensure}\:{that} \\ $$$${this}\:{number}\:{is}\:{a}\:{prime}\:{number}\:{or}\:{a}\:{composite}\:{number}\:? \\ $$ Commented by Rasheed Soomro last updated on 29/Jul/16 $$\mathrm{97} \\ $$$${The}\:{largest}\:{prime}\:{number}\:{not}\:{greater}\:{than}\:\sqrt{\mathrm{9631}}…

Question-137876

Question Number 137876 by Bekzod Jumayev last updated on 07/Apr/21 Answered by MJS_new last updated on 07/Apr/21 $$\int\frac{{dx}}{\left({x}^{\mathrm{3}} −\mathrm{1}\right)^{\mathrm{1}/\mathrm{3}} }= \\ $$$$\:\:\:\:\:\left[{t}=\frac{{x}}{\left({x}^{\mathrm{3}} −\mathrm{1}\right)^{\mathrm{1}/\mathrm{3}} }\:\rightarrow\:{dx}=−\left({x}^{\mathrm{3}} −\mathrm{1}\right)^{\mathrm{4}/\mathrm{3}}…

given-that-y-ln-1-cos-2-x-find-dy-dx-at-the-point-x-3pi-4-and-if-y-ln-x-2-4-find-dy-dx-at-x-1-

Question Number 72343 by Rio Michael last updated on 27/Oct/19 $${given}\:{that}\:{y}\:=\:{ln}\:\left(\:\mathrm{1}\:+\:{cos}^{\mathrm{2}} {x}\right)\:{find}\:\frac{{dy}}{{dx}\:\:}\:{at}\:{the}\:{point}\:\:{x}\:=\:\frac{\mathrm{3}\pi}{\mathrm{4}} \\ $$$${and}\:\:{if}\:\:{y}\:={ln}\left({x}^{\mathrm{2}} \:+\:\mathrm{4}\right)\:{find}\:\:\frac{{dy}}{{dx}}\:{at}\:{x}\:=\:\mathrm{1} \\ $$ Commented by mathmax by abdo last updated on…

Question-6806

Question Number 6806 by Tawakalitu. last updated on 27/Jul/16 Answered by Yozzii last updated on 28/Jul/16 $${We}\:{have}\:{that}\:\angle{QSR}=\mathrm{40}°.\:{Let}\:\omega\:{be}\: \\ $$$${circle}\:{PQRS}.\:{Points}\:{S}\:{and}\:{P}\:{lie}\:{on} \\ $$$$\omega\:{on}\:{the}\:{same}\:{side}\:{of}\:{line}\:{QR}.\: \\ $$$$\Rightarrow\angle{QSR}=\angle{QPR}\:\therefore\:\angle{QPR}=\mathrm{40}°. \\ $$$${TU}\:{is}\:{a}\:{straight}\:{line},\:{so}\:…

nice-calculus-n-1-sin-nx-n-pi-2-x-2-Im-1-e-ix-Imln-1-cos-x-isin-x-Im-ln-1-cos-x-2-sin-2-x-itan-1

Question Number 137873 by mnjuly1970 last updated on 07/Apr/21 $$\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:…….{nice}\:\:…………{calculus}……. \\ $$$$\:\:\:\:\boldsymbol{\phi}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{sin}\left({nx}\right)}{{n}}\:=\frac{\pi}{\mathrm{2}}−\frac{{x}}{\mathrm{2}} \\ $$$$\:\:\:\boldsymbol{\phi}=−{Im}\left(\mathrm{1}−{e}^{{ix}} \right)=−{Imln}\left\{\left(\mathrm{1}−{cos}\left({x}\right)−{isin}\left({x}\right)\right)\right\} \\ $$$$\:\:\:\:=−{Im}\left\{{ln}\left(\sqrt{\left(\mathrm{1}−{cos}\left({x}\right)\right)^{\mathrm{2}} +{sin}^{\mathrm{2}} \left({x}\right)}\:+{itan}^{−\mathrm{1}} \left(\frac{−{sin}\left({x}\right)}{\mathrm{1}−{cos}\left({x}\right)}\right)\right\}\right. \\…

x-4x-16x-4-2019-x-3-x-1-

Question Number 72339 by naka3546 last updated on 27/Oct/19 $$\sqrt{{x}\:+\:\sqrt{\mathrm{4}{x}\:+\:\sqrt{\mathrm{16}{x}\:+\:…\:+\:\sqrt{\mathrm{4}^{\mathrm{2019}} {x}\:+\:\mathrm{3}}}}}\:\:=\:\:\sqrt{{x}}\:+\:\mathrm{1} \\ $$ Commented by naka3546 last updated on 27/Oct/19 $${x}\:\:=\:\:? \\ $$ Terms of…