Question Number 222044 by wewji12 last updated on 15/Jun/25 $$\mathrm{How}\:\mathrm{do}\:\mathrm{you}\:\mathrm{evaluate} \\ $$$$\int_{−\infty} ^{\:\:\infty} \:\:\frac{\mathrm{sin}\left({z}+\mathrm{1}\right)}{\left({z}+\mathrm{1}\right)\left({z}^{\mathrm{2}} +\mathrm{1}\right)}\:\mathrm{d}{z} \\ $$ Answered by vnm last updated on 15/Jun/25 $$…
Question Number 222031 by fantastic last updated on 15/Jun/25 $${x}^{{x}} =−\mathrm{1} \\ $$$${Number}\:{of}\:{solutions}?? \\ $$ Answered by mr W last updated on 15/Jun/25 $${solve}\:\boldsymbol{{z}}^{\boldsymbol{{z}}} =−\mathrm{1}{for}\:\boldsymbol{{z}}\in\boldsymbol{{C}}.…
Question Number 222025 by fantastic last updated on 15/Jun/25 $$\left(\frac{\mathrm{5cos}\:^{\mathrm{2}} \frac{\pi}{\mathrm{3}}+\mathrm{4sec}\:^{\mathrm{2}} \frac{\pi}{\mathrm{6}}−\mathrm{tan}\:^{\mathrm{2}} \frac{\pi}{\mathrm{4}}}{\mathrm{sin}\:^{\mathrm{2}} \frac{\pi}{\mathrm{6}}+\mathrm{cos}\:^{\mathrm{2}} \frac{\pi}{\mathrm{6}}}\right)=?? \\ $$$$\left[{easy}\:{mode}\right] \\ $$ Answered by MrGaster last updated on…
Question Number 222026 by fantastic last updated on 15/Jun/25 $${If}\:\left(\mathrm{1}.\mathrm{234}\right)^{{a}} =\left(\mathrm{0}.\mathrm{1234}\right)^{{b}} =\mathrm{10}^{{c}} \\ $$$${prove}\:{that}\:\frac{\mathrm{1}}{{a}}−\frac{\mathrm{1}}{{c}}=\frac{\mathrm{1}}{{b}} \\ $$ Answered by som(math1967) last updated on 15/Jun/25 $$\left(\mathrm{1}.\mathrm{234}\right)^{{a}} =\left(\mathrm{0}.\mathrm{1234}\right)^{{b}}…
Question Number 222022 by fantastic last updated on 15/Jun/25 $${If}\:\angle{P}+\angle{Q}\:=\mathrm{90}^{\mathrm{0}} \:{then}\:{prove}\:{that} \\ $$$$\sqrt{\frac{\mathrm{sin}\:{P}}{\mathrm{cos}\:{Q}}−\mathrm{sin}\:{P}\mathrm{cos}\:{Q}}=\mathrm{cos}\:{P} \\ $$ Commented by MathematicalUser2357 last updated on 17/Jun/25 $${You}\:{mean}\:{If}\:\angle{P}+\angle{Q}\:=\mathrm{222022}^{\mathrm{0}} \:{then}\:{prove}\:{that} \\…
Question Number 222019 by Nicholas666 last updated on 15/Jun/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\pi} \:\mathrm{tan}^{−\mathrm{1}} \:\left(\frac{\mathrm{ln}\left(\mathrm{sin}\left({x}\right)\right.}{{x}}\right)\:{dx} \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 221981 by MrGaster last updated on 14/Jun/25 $$\mathrm{Prove}:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{n}^{\mathrm{3}} }{{e}^{\mathrm{2}\pi{n}} −\mathrm{1}}=\frac{\Gamma\left(\frac{\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{8}} }{\mathrm{5120}\pi^{\mathrm{6}} }−\frac{\mathrm{1}}{\mathrm{240}}=\frac{\mathrm{1}}{\mathrm{80}}\left(\frac{\varpi}{\pi}\right)^{\mathrm{4}} −\frac{\mathrm{1}}{\mathrm{240}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 221973 by ajfour last updated on 14/Jun/25 $$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }+{y}={k}−\frac{\mathrm{1}}{{x}^{\mathrm{2}} }−\frac{\mathrm{6}}{{x}^{\mathrm{4}} }\:\:\:\:\:\: \\ $$$${Find}\:{y}\left({x}\right)\:\:\:\:\left({k}\:{is}\:{constant}\right). \\ $$ Answered by mahdipoor last updated on 14/Jun/25…
Question Number 222007 by klipto last updated on 14/Jun/25 $$\boldsymbol{\mathrm{x}}\sqrt{\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} }+\boldsymbol{\mathrm{log}}\left(\boldsymbol{\mathrm{x}}+\sqrt{\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\right)=\mathrm{12}.\mathrm{5} \\ $$$$\mathrm{find}\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:\left(\mathrm{answer}\:\mathrm{should}\:\mathrm{not}\:\mathrm{be}\:\mathrm{in}\:\mathrm{decimal}\right) \\ $$ Commented by AntonCWX8 last updated on 15/Jun/25 $${Do}\:{you}\:{mean}\:{to}\:{find}\:{a}\:{close}\:{form}?…
Question Number 221968 by MathematicalUser2357 last updated on 14/Jun/25 $$\left({a}+{b}+{c}\right)^{\mathrm{3}} \\ $$ Answered by MrGaster last updated on 14/Jun/25 Commented by MathematicalUser2357 last updated on…