Question Number 163564 by HongKing last updated on 07/Jan/22 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{closed}\:\mathrm{form}\:\mathrm{of}\:\mathrm{a}\:\mathrm{integral}: \\ $$$$\boldsymbol{\Omega}\:\:=\:\underset{\:\frac{\boldsymbol{\pi}}{\mathrm{2}}} {\overset{\:\boldsymbol{\pi}} {\int}}\:\frac{\mathrm{dx}}{\mathrm{e}^{\boldsymbol{\mathrm{x}}} \:+\:\mathrm{ln}\:\left(\mathrm{cos}\boldsymbol{\mathrm{x}}\right)} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 163548 by HongKing last updated on 07/Jan/22 $$\mathrm{Lambert}\:\mathrm{series}\:\mathrm{type}\:\mathrm{representation} \\ $$$$\mathrm{for}\:\:\sqrt{-\mathrm{1}}\:\:\mathrm{factorial} \\ $$$$\left(\mathrm{i}^{\boldsymbol{\mathrm{i}}} \right)!\:\left(-\mathrm{i}^{\boldsymbol{\mathrm{i}}} \right)!\:=\:\mathrm{1}\:-\:\mathrm{2}\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\left(-\mathrm{1}\right)^{\boldsymbol{\mathrm{n}}} }{\mathrm{e}^{\boldsymbol{\pi}} \:\mathrm{n}^{\mathrm{2}} \:-\:\mathrm{1}} \\ $$ Terms of…
Question Number 163536 by HongKing last updated on 07/Jan/22 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\underset{\:\mathrm{9}} {\overset{\:\mathrm{1}} {\int}}\:\frac{\mathrm{ln}\:\left(\mathrm{1}\:+\:\mathrm{x}\right)}{\mathrm{1}\:+\:\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx}\:=\:\frac{\pi\:\centerdot\:\mathrm{ln}\:\left(\mathrm{2}\right)}{\mathrm{8}} \\ $$ Answered by Ar Brandon last updated on 07/Jan/22…
Question Number 32446 by Mr eaay last updated on 25/Mar/18 Answered by MJS last updated on 25/Mar/18 $$\mathrm{left}\:\mathrm{side}: \\ $$$$\mathrm{8}^{\frac{\left({x}−\mathrm{1}\right){x}^{\mathrm{2}{x}} }{{x}^{{x}} \left({x}−\mathrm{2}\right)}} ×\mathrm{16}^{{x}^{{x}} } =\mathrm{8}^{\frac{\left({x}−\mathrm{1}\right){x}^{{x}}…
Question Number 32441 by jasno91 last updated on 25/Mar/18 Answered by MJS last updated on 25/Mar/18 $$\left(\mathrm{1}−\left(\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}\right)\right)×\mathrm{5}\frac{\mathrm{1}}{\mathrm{2}}{m}= \\ $$$$=\left(\mathrm{1}−\left(\frac{\mathrm{4}}{\mathrm{12}}+\frac{\mathrm{3}}{\mathrm{12}}\right)\right)×\frac{\mathrm{11}}{\mathrm{2}}{m}= \\ $$$$=\left(\frac{\mathrm{12}}{\mathrm{12}}−\frac{\mathrm{7}}{\mathrm{12}}\right)×\frac{\mathrm{11}}{\mathrm{2}}{m}=\frac{\mathrm{5}}{\mathrm{12}}×\frac{\mathrm{11}}{\mathrm{2}}{m}= \\ $$$$=\frac{\mathrm{55}}{\mathrm{24}}{m}=\mathrm{2}\frac{\mathrm{7}}{\mathrm{24}}{m} \\ $$…
Question Number 97968 by HamraboyevFarruxjon last updated on 11/Jun/20 $$ \\ $$ Commented by 06122004 last updated on 10/Jun/20 Osonmasmi �� Answered by 1549442205 last updated…
Question Number 32424 by Tinkutara last updated on 24/Mar/18 Answered by mrW2 last updated on 24/Mar/18 $$\frac{\mathrm{6}!}{\mathrm{2}!\mathrm{2}!}−\mathrm{2}×\left(\frac{\mathrm{5}!}{\mathrm{2}!}−\mathrm{4}!\right)−\mathrm{4}!=\mathrm{84} \\ $$$$\Rightarrow{answer}\:\left(\mathrm{3}\right) \\ $$ Commented by Tinkutara last…
Question Number 97936 by bobhans last updated on 10/Jun/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\sqrt{\mathrm{45}−\sqrt{\mathrm{2000}}\:}\:\:+\:\:\sqrt{\mathrm{45}+\sqrt{\mathrm{2000}}}\: \\ $$ Commented by pranesh last updated on 10/Jun/20 $${find}\:{y} \\ $$ Answered…
Question Number 163470 by eman_64 last updated on 07/Jan/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 32395 by saru53424@gmail.com last updated on 24/Mar/18 $$\mathrm{1}+\mathrm{1} \\ $$ Commented by abdo imad last updated on 24/Mar/18 $$\mathrm{1}+\mathrm{1}\:=\mathrm{2}\:{inside}\:{k}\:/{car}\left({k}\right)\neq\mathrm{2} \\ $$$$\mathrm{1}+\mathrm{1}\:=\mathrm{0}\:{inside}\:{Z}/\mathrm{2}{Z} \\ $$$$\mathrm{1}+\mathrm{1}\:=−\mathrm{1}\:{inside}\:{Z}/\mathrm{3}{Z}….…