Question Number 64640 by Tawa1 last updated on 19/Jul/19 $$\mathrm{I}\:\:=\:\:\underset{\mathrm{n}\:=\:\mathrm{0}} {\overset{\infty} {\sum}}\:\:\frac{\left(−\:\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{6n}\:+\:\mathrm{1}} \\ $$ Commented by mathmax by abdo last updated on 20/Jul/19 $${let}\:\:{S}\left({x}\right)\:=\sum_{{n}=\mathrm{0}}…
Question Number 130173 by mohammad17 last updated on 23/Jan/21 Commented by mohammad17 last updated on 23/Jan/21 $$????? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 64635 by mathmax by abdo last updated on 19/Jul/19 $$\left.\mathrm{1}\right){calculate}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\frac{{arctan}\left(\alpha{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}\:\:{with}\:\alpha\:{real} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left(\mathrm{2}{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$ Commented by mathmax…
Question Number 130168 by Adel last updated on 23/Jan/21 $$\mathrm{log}\underset{\mathrm{X}} {\mathrm{2}}\centerdot\mathrm{log}\:\underset{\mathrm{2X}} {\mathrm{2}}=\mathrm{log}\:\underset{\mathrm{4X}} {\mathrm{2}}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{X}=? \\ $$ Commented by liberty last updated on 23/Jan/21 $$\mathrm{do}\:\mathrm{you}\:\mathrm{meant}\:\mathrm{log}\:_{{x}} \left(\mathrm{2}\right).\mathrm{log}\:_{\mathrm{2}{x}} \left(\mathrm{2}\right)\:=\:\mathrm{log}\:_{\mathrm{4}{x}}…
Question Number 130169 by BHOOPENDRA last updated on 23/Jan/21 $$\frac{\mathrm{1}}{{s}}{log}\frac{\left({s}−\mathrm{2}\right)}{\left({s}−\mathrm{3}\right)}\:{find}\:{inverse}\:{laplace} \\ $$ Answered by Olaf last updated on 23/Jan/21 $$\mathrm{F}\left({s}\right)\:=\:\frac{\mathrm{1}}{{s}}\mathrm{ln}\frac{{s}−\mathrm{2}}{{s}−\mathrm{3}} \\ $$$$\mathrm{F}\left({s}\right)\:=\:\frac{{s}−\mathrm{2}}{{s}}.\frac{\mathrm{ln}\left({s}−\mathrm{2}\right)}{{s}−\mathrm{2}}−\frac{{s}−\mathrm{3}}{{s}}.\frac{\mathrm{ln}\left({s}−\mathrm{3}\right)}{{s}−\mathrm{3}} \\ $$$$\mathrm{F}\left({s}\right)\:=\:\left(\frac{\mathrm{2}}{{s}}−\mathrm{1}\right)\left\{−\frac{\mathrm{1}}{{s}−\mathrm{2}}\left[\mathrm{ln}\left({s}−\mathrm{2}\right)+\gamma\right]\right\} \\…
Question Number 64631 by Mikael last updated on 19/Jul/19 $$\sqrt{\frac{\mathrm{1}+\mathrm{2}{x}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{\mathrm{2}}}+\mathrm{2}{x}^{\mathrm{2}} =\mathrm{1} \\ $$$$\mathrm{To}\:\mathrm{solve}\:\mathrm{in}\:\mathbb{R} \\ $$ Commented by behi83417@gmail.com last updated on 20/Jul/19 $$−\mathrm{1}<\mathrm{x}\leqslant\mathrm{1},\mathrm{let}:\:\mathrm{x}=\mathrm{cost} \\…
Question Number 130167 by Lordose last updated on 23/Jan/21 $$\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{ln}\left(\mathrm{u}\right)\mathrm{e}^{−\mathrm{u}} }{\left(\mathrm{1}+\mathrm{e}^{−\mathrm{u}} \right)^{\mathrm{2}} }\mathrm{du} \\ $$$$ \\ $$$$ \\ $$ Answered by mindispower last…
Question Number 64625 by ajfour last updated on 19/Jul/19 Commented by ajfour last updated on 19/Jul/19 $${Are}\:{AD},\:{BE},\:{CF}\:\:{concurrent} \\ $$$${generally}?\:{please}\:{help}\:{check}. \\ $$ Commented by MJS last…
Question Number 130158 by benjo_mathlover last updated on 23/Jan/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{segment}\:\mathrm{of}\:\mathrm{the}\:\mathrm{curve} \\ $$$$\mathrm{y}^{\mathrm{2}} \:=\:\:\:\mathrm{x}^{\mathrm{3}} −\mathrm{x}^{\mathrm{2}} \:\mathrm{if}\:\mathrm{the}\:\mathrm{line}\:\mathrm{x}=\:\:\:\mathrm{2}\:\mathrm{is}\:\mathrm{the}\:\mathrm{chord}\: \\ $$$$\mathrm{determining}\:\mathrm{the}\:\mathrm{segment}\: \\ $$ Answered by liberty last updated on…
Question Number 64619 by Aysha Abedin last updated on 19/Jul/19 $${show}\:{that}\:\int_{−\alpha} ^{\alpha} {sinc}\left({x}\right){dx}=\int_{−\alpha} ^{\alpha} {sinc}^{\mathrm{2}} \left({x}\right){dx}=\Pi \\ $$ Commented by mathmax by abdo last updated…