Question Number 222937 by Nicholas666 last updated on 11/Jul/25 $$ \\ $$$$\:\:\:\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{following}\:\mathrm{identity}\:\mathrm{holds}\::\:\:\:\: \\ $$$$\:\:\:\underset{\lambda\in\mathbb{Z}\left[{i}\right]} {\sum}\:\left(\frac{\mathrm{1}}{\left(\mathrm{1}\:+\:\mathrm{3}\lambda\right)^{\mathrm{3}} }\right)\:=\:\frac{\pi^{\mathrm{9}/\mathrm{2}} \:\sqrt{\mathrm{1}\:+\:\sqrt{\mathrm{3}\:}}}{\mathrm{2}^{\mathrm{5}/\mathrm{4}} \:\:\mathrm{3}^{\mathrm{27}/\mathrm{8}} \:\Gamma\left(\frac{\mathrm{3}}{\mathrm{4}}\right)^{\mathrm{6}} \:}\:\:\:\:\: \\ $$$$\:\:\:\:\mathrm{Where}\:\mathbb{Z}\left[{i}\right]\:=\:\left\{{a}\:+\:{bi}\::\:{a},{b}\:\in\:\mathbb{Z}\right\}\:\mathrm{denotes}\:\mathrm{gaussian}\:\mathrm{integers}\:!\:\:\:\:\:\:\:\:\: \\ $$$$\: \\…
Question Number 222954 by klipto last updated on 11/Jul/25 $$ \\ $$ Commented by klipto last updated on 11/Jul/25 Commented by gabthemathguy25 last updated on…
Question Number 222955 by ajfour last updated on 11/Jul/25 Commented by ajfour last updated on 11/Jul/25 $${Find}\:{the}\:{side}\:{length}\:{of}\:\:{square}\:{ABCD},\:{if} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{when}\:{it}\:{is}\:{a}\:{square}. \\ $$ Answered by mr W…
Question Number 222929 by gabthemathguy25 last updated on 11/Jul/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 222908 by Nicholas666 last updated on 10/Jul/25 Answered by Ak090 last updated on 10/Jul/25 $${d}/{dx}\:{ln}\left({cosh}\:{x}\right)\:=\:{tanh}\:{x} \\ $$$${d}/{dx}\:^{{p}} \sqrt{{x}}\:\mathrm{using}\:\mathrm{the}\:\mathrm{formula}\:{d}/{dx}\:{f}^{−\mathrm{1}} \left({x}\right) \\ $$$$=\:\mathrm{1}/{f}'\left({f}^{−\mathrm{1}} \left({x}\right)\right)\:=\:\mathrm{1}/{px}^{\left({p}−\mathrm{1}\right)/{p}} \\…
Question Number 222876 by pranapatiaditya last updated on 10/Jul/25 $$\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{2}{y}} ^{\mathrm{2}} {e}^{{x}^{\mathrm{2}} } {dxdy}=? \\ $$ Answered by MrGaster last updated on 10/Jul/25…
Question Number 222879 by MrGaster last updated on 10/Jul/25 Answered by gabthemathguy25 last updated on 10/Jul/25 $$\approx\mathrm{1}.\mathrm{67215} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 222874 by gabthemathguy25 last updated on 10/Jul/25 $$\mathrm{evaluate}\:\mathrm{the}\:\mathrm{following}\:\mathrm{integral} \\ $$$$\int\frac{{x}^{\mathrm{5}} \mathrm{ln}\left({x}\right)}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{3}} }\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 222867 by MrGaster last updated on 10/Jul/25 $$\int_{−\pi} ^{\pi} {x}\:\mathrm{sin}\:{x}\:\mathrm{cos}{nxdx} \\ $$ Answered by MrGaster last updated on 10/Jul/25 Commented by wewji12 last…
Question Number 222921 by cherokeesay last updated on 10/Jul/25 Answered by mr W last updated on 11/Jul/25 Commented by mr W last updated on 11/Jul/25…