Question Number 218582 by Nicholas666 last updated on 12/Apr/25 $$ \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\infty} \:\frac{{cos}\left({ax}\right)\:−\:{cos}\left({bx}\right)}{{x}^{\mathrm{2}} }\:{dx}\:=\:\frac{\pi}{\mathrm{2}}\:\mid{b}−{a}\mid\: \\ $$$$ \\ $$ Answered by aleks041103 last updated on…
Question Number 218583 by Nicholas666 last updated on 12/Apr/25 $$ \\ $$$$\:\int_{\mathrm{0}\:} ^{\infty} \:{e}^{−{x}} \:\left(\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{{f}\left({n}\right)}{{n}}\:{sin}\left({nx}\right)\right){dx}\:=\mathrm{1} \\ $$$$ \\ $$ Answered by aleks041103 last…
Question Number 218578 by mr W last updated on 13/Apr/25 $$\mathrm{10}\:{couples}\:{are}\:{invited}\:{to}\:{a}\:{dinner}. \\ $$$${after}\:{the}\:{dinner}\:{they}\:{form}\:{pairs}\: \\ $$$${to}\:{dance}.\:{in}\:{how}\:{many}\:{ways}\:{can}\:{they} \\ $$$${do}\:{this}, \\ $$$$\left.\mathrm{1}\right)\:{generally} \\ $$$$\left.\mathrm{2}\right)\:{a}\:{man}\:{should}\:{dance}\:{with}\:{a}\:{woman} \\ $$$$\left.\mathrm{3}\left.\right)\:{as}\:\mathrm{2}\right),\:{but}\:{two}\:{special}\:{couples} \\ $$$$\:\:\:\:\:{should}\:{not}\:{dance}\:{with}\:{each}\:{other}…
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Question Number 218606 by Spillover last updated on 12/Apr/25 Answered by A5T last updated on 13/Apr/25 Commented by A5T last updated on 13/Apr/25 $$\angle\mathrm{BAF}=\alpha\:\Rightarrow\:\angle\mathrm{ABF}=\alpha\:\mathrm{since}\:\mathrm{BF}=\mathrm{AF} \\…
Question Number 218607 by Spillover last updated on 13/Apr/25 Answered by mr W last updated on 13/Apr/25 Commented by mr W last updated on 13/Apr/25…
Question Number 218603 by hardmath last updated on 12/Apr/25 Commented by mr W last updated on 13/Apr/25 $${seems}\:{true} \\ $$ Commented by mr W last…
Question Number 218596 by SdC355 last updated on 12/Apr/25 $$\mathrm{why}\:\mathrm{my}\:\mathrm{answer}\:\mathrm{is}\:\mathrm{delete}???? \\ $$$$\mathrm{Tinkutara}\:\mathrm{why}\:\mathrm{you}\:\mathrm{ignore}\:\mathrm{my}\:\mathrm{effort} \\ $$ Commented by Ghisom last updated on 12/Apr/25 $$\mathrm{maybe}\:\mathrm{post}\:\mathrm{your}\:\mathrm{answer}\:\mathrm{as}\:\mathrm{answer}\:\mathrm{to} \\ $$$$\mathrm{the}\:\mathrm{question}\:\mathrm{instead}\:\mathrm{of}\:\mathrm{opening}\:\mathrm{a}\:\mathrm{new} \\…
Question Number 218598 by Nicholas666 last updated on 12/Apr/25 $$ \\ $$$$\:\:\:\underset{\mathrm{0}} {\int}^{\infty} \:\frac{\boldsymbol{{x}}}{\boldsymbol{{sinh}}\left(\boldsymbol{{x}}\right)}\boldsymbol{{ln}}\left(\frac{\boldsymbol{{x}}}{\boldsymbol{{e}}^{\boldsymbol{{x}}} −\mathrm{1}}\right)\boldsymbol{{dx}}\: \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 218599 by Nicholas666 last updated on 12/Apr/25 $$ \\ $$$$\:\:\:\int_{\mathrm{0}} ^{\infty} \boldsymbol{{x}}^{\boldsymbol{{s}}−\mathrm{1}} \:\underset{\boldsymbol{{n}}=\mathrm{1}\:} {\overset{\infty} {\prod}}\left(\mathrm{1}−\boldsymbol{{e}}^{−\boldsymbol{{nx}}} \right)^{−\mathrm{24}} \:\boldsymbol{{dx}} \\ $$$$ \\ $$ Commented by…