Question Number 152866 by talminator2856791 last updated on 02/Sep/21 $$\: \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\int_{−\infty} ^{\:\infty} \:\frac{\mathrm{ln}\left(\sqrt{{x}^{\mathrm{4}} +\mathrm{1}}\right)}{\left(\mathrm{ln}\left(\left(\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\right)^{\mathrm{3}} \right)\right)^{\mathrm{2}} }\:\:{dx} \\ $$$$\: \\ $$$$\: \\…
Question Number 152861 by talminator2856791 last updated on 02/Sep/21 $$\: \\ $$$$\:\:\:\:\:\:\: \\ $$$$\int_{−\infty} ^{\:\infty} \frac{\left(\mathrm{ln}\left(\left({x}^{\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}} +\mathrm{1}\right)^{\mathrm{2}} +\mathrm{1}\right)\right)^{−\mathrm{ln}\left({x}^{\mathrm{2}} +\mathrm{1}\right)} }{\:\sqrt{{x}^{\mid\lfloor{x}\rfloor\mid} +\mathrm{1}}}\:\:{dx} \\ $$$$\: \\…
Question Number 152863 by talminator2856791 last updated on 02/Sep/21 $$\: \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\int_{−\infty} ^{\:\infty} \:\frac{\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}\:\:{dx} \\ $$$$\: \\ $$$$\: \\ $$ Commented by…
Question Number 87325 by M±th+et£s last updated on 04/Apr/20 $$\left.\mathrm{1}\right)\:\int{e}^{\sqrt{{x}}} \:{dx} \\ $$$$\left.\mathrm{2}\right)\int\frac{\sqrt{{sin}\left({x}\right)}}{\:\sqrt{{sin}\left({x}\right)}+\sqrt{{cos}\left({x}\right)}}{dx} \\ $$ Commented by Serlea last updated on 04/Apr/20 $$\left.\mathrm{1}\right)\:\int\mathrm{e}^{\sqrt{\mathrm{x}}} \mathrm{dx} \\…
Question Number 152857 by Tawa11 last updated on 02/Sep/21 An electric current passes through two voltmeters in series containing copper sulphate (CuSO₄) and silver nitrate…
Question Number 87322 by peter frank last updated on 04/Apr/20 $$\mathrm{I}{nvestigate}\:{the}\:{stationary} \\ $$$${value}\:{of} \\ $$$$\frac{{x}^{\mathrm{3}} }{\mathrm{1}+{x}^{\mathrm{2}} }\:{and}\:{sketch}\:{the}\:{graph} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 152856 by Olaf_Thorendsen last updated on 02/Sep/21 $$\mathrm{Monsieur}\:\mathrm{Puissant},\:\mathrm{je}\:\mathrm{quitte}\:\mathrm{ce}\:\mathrm{forum} \\ $$$$\mathrm{math}\acute {\mathrm{e}matique}\:\mathrm{d}\acute {\mathrm{e}finitivement}\:\mathrm{mais} \\ $$$$\mathrm{sans}\:\mathrm{avoir}\:\mathrm{dit}\:\mathrm{que}\:\mathrm{j}'\mathrm{ai}\:\mathrm{ador}\acute {\mathrm{e}}\:\acute {\mathrm{e}changer} \\ $$$$\mathrm{avec}\:\mathrm{vous}. \\ $$$$ \\ $$$$\mathrm{Bonne}\:\mathrm{continuation}\:\mathrm{et}\:\mathrm{vive}\:\mathrm{les} \\…
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Question Number 21784 by Tinkutara last updated on 03/Oct/17 $$\mathrm{Call}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{integer}\:{n}\:\boldsymbol{\mathrm{good}}\:\mathrm{if}\:\mathrm{there} \\ $$$$\mathrm{are}\:{n}\:\mathrm{integers},\:\mathrm{positive}\:\mathrm{or}\:\mathrm{negative},\:\mathrm{and} \\ $$$$\mathrm{not}\:\mathrm{necessarily}\:\mathrm{distinct},\:\mathrm{such}\:\mathrm{that}\:\mathrm{their} \\ $$$$\mathrm{sum}\:\mathrm{and}\:\mathrm{product}\:\mathrm{are}\:\mathrm{both}\:\mathrm{equal}\:\mathrm{to}\:{n} \\ $$$$\left(\mathrm{e}.\mathrm{g}.\:\mathrm{8}\:\mathrm{is}\:\boldsymbol{\mathrm{good}}\:\mathrm{since}\right. \\ $$$$\mathrm{8}=\mathrm{4}\centerdot\mathrm{2}\centerdot\mathrm{1}\centerdot\mathrm{1}\centerdot\mathrm{1}\centerdot\mathrm{1}\left(−\mathrm{1}\right)\left(−\mathrm{1}\right)=\mathrm{4}+\mathrm{2}+\mathrm{1}+\mathrm{1}+\mathrm{1} \\ $$$$\left.+\mathrm{1}+\left(−\mathrm{1}\right)+\left(−\mathrm{1}\right)\right). \\ $$$$\mathrm{Show}\:\mathrm{that}\:\mathrm{integers}\:\mathrm{of}\:\mathrm{the}\:\mathrm{form}\:\mathrm{4}{k}\:+\:\mathrm{1} \\…
Question Number 21782 by drbl.gnbd last updated on 03/Oct/17 $${a}_{\mathrm{1}} =\mathrm{1},\:{a}_{{n}+\mathrm{1}} =\frac{{a}_{{n}} }{\:\sqrt{{a}_{{n}} +{n}+\mathrm{1}}} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{a}_{{n}} =? \\ $$ Terms of Service Privacy…