Question Number 137838 by Bekzod Jumayev last updated on 07/Apr/21 $$\int{log}_{{x}} {edx}=?? \\ $$ Commented by mr W last updated on 07/Apr/21 $$=\int\frac{\mathrm{1}}{\mathrm{ln}\:{x}}{dx} \\ $$$$={li}\left({x}\right)+{C}…
Question Number 6762 by 314159 last updated on 24/Jul/16 Commented by Yozzii last updated on 24/Jul/16 $${x}_{\mathrm{1}} ^{\mathrm{2}} +{x}_{\mathrm{2}} ^{\mathrm{2}} +\mathrm{2}{x}_{\mathrm{1}} {x}_{\mathrm{2}} {cos}\theta=\mathrm{1}, \\ $$$${y}_{\mathrm{1}}…
Question Number 72296 by naka3546 last updated on 27/Oct/19 $${Let}\:\:\:\:{x}\:\:=\:\:{f}\left({x}\right)\:{e}^{{f}\left({x}\right)} \\ $$$$\:\:\:\:\:\:\underset{\:\mathrm{0}} {\int}\overset{\:{e}} {\:}{f}\left({x}\right)\:{dx}\:\:=\:\:? \\ $$ Commented by naka3546 last updated on 27/Oct/19 $${e}^{\mathrm{ln}\:{x}} \:\:=\:\:{x}…
Question Number 137829 by mnjuly1970 last updated on 07/Apr/21 $$\:\:\:\:\:…….{nice}\:\:…\:…\:….\:{calculus}….. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{prove}\:{that}\::::: \\ $$$$\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \left(\frac{{log}\left(\mathrm{1}−{x}\right)}{{x}}\right)^{\mathrm{2}} {dx}=\mathrm{2}\zeta\left(\mathrm{2}\right)…. \\ $$$$ \\ $$ Answered by EnterUsername last…
Question Number 72294 by mr W last updated on 27/Oct/19 Commented by mr W last updated on 27/Oct/19 $${the}\:{distances}\:{from}\:{a}\:{point}\:{to}\:{three} \\ $$$${vertices}\:{of}\:{a}\:{square}\:{are}\:{known}. \\ $$$${find}\:{the}\:{side}\:{length}\:{of}\:{the}\:{square}. \\ $$…
Question Number 6758 by FilupSmith last updated on 23/Jul/16 $$\mathrm{A}\:\mathrm{circle}\:\mathrm{of}\:\mathrm{radius}\:{r}\:\mathrm{has}\:\mathrm{a}\:\mathrm{point}\:{O}\:\mathrm{as}\:\mathrm{its} \\ $$$$\mathrm{centre}.\:\mathrm{Points}\:{A}\:\mathrm{and}\:{B}\:\mathrm{are}\:\mathrm{points}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{circumference}. \\ $$$$ \\ $$$$\mathrm{For}\:\bigtriangleup{OAB},\:\overline {{OA}}=\overline {{OB}}={r},\:\overline {{AB}}={d},\:\angle{AOB}=\theta. \\ $$$$\mathrm{What}\:\mathrm{is}\:\frac{{r}}{{d}}? \\ $$…
Question Number 72291 by aliesam last updated on 27/Oct/19 Answered by mr W last updated on 27/Oct/19 $$\left(\mathrm{5}{m}\:\mathrm{sin}\:\left(\mathrm{3}{x}\right)\right)^{\mathrm{2}} =\left(\mathrm{4}\:\mathrm{sin}\:{x}\right)^{\mathrm{2}} \\ $$$$\mathrm{5}{m}\:\mathrm{sin}\:\left(\mathrm{3}{x}\right)=\pm\mathrm{4}\:\mathrm{sin}\:{x} \\ $$$$\mathrm{5}{m}\:\mathrm{sin}\:{x}\:\left(\mathrm{3}−\mathrm{4}\:\mathrm{sin}^{\mathrm{2}} \:{x}\right)=\pm\mathrm{4}\:\mathrm{sin}\:{x} \\…
Question Number 72289 by mathocean1 last updated on 27/Oct/19 $${Bonjour}. \\ $$$${Aidez}\:{moi}\:{a}\:{resoudre}\:{le}\:{systeme}\: \\ $$$${suivant}\:\:\:\:{dans}\:\mathbb{R}^{\mathrm{2}} \:\:\:\:\: \\ $$$${x}−{y}=\mathrm{2} \\ $$$${xy}=\mathrm{20} \\ $$ Answered by mr W…
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Question Number 137820 by bramlexs22 last updated on 07/Apr/21 $$\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}−\mathrm{tan}\:\frac{{x}}{\mathrm{2}}\right)\left(\mathrm{1}−\mathrm{sin}\:{x}\right)}{\left(\mathrm{1}+\mathrm{tan}\:\frac{{x}}{\mathrm{2}}\right)\left(\pi−\mathrm{2}{x}\right)^{\mathrm{3}} }\:? \\ $$ Answered by SLVR last updated on 07/Apr/21 Commented by SLVR last…