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Question Number 224233 Answers: 1 Comments: 0
$$\mathrm{Prove}\:\mathrm{that}\:\forall\mathrm{n}\geqslant\mathrm{2} \\ $$$$\mathrm{e}^{\mathrm{2n}−\mathrm{1}} −\mathrm{1}\:\geqslant\:\mathrm{2n}\left(\mathrm{2n}−\mathrm{1}\right) \\ $$
Question Number 224229 Answers: 1 Comments: 1
Question Number 224225 Answers: 0 Comments: 0
Question Number 224224 Answers: 0 Comments: 3
Question Number 224213 Answers: 1 Comments: 1
Question Number 224207 Answers: 0 Comments: 5
Question Number 224203 Answers: 0 Comments: 6
Question Number 224201 Answers: 0 Comments: 0
$$\int\:\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{x}^{\mathrm{7}} −\mathrm{8x}^{\mathrm{2}} }\:\mathrm{dx} \\ $$
Question Number 224191 Answers: 0 Comments: 1
Question Number 224197 Answers: 2 Comments: 0
$$\int_{\mathrm{0}} ^{\infty} \left(\boldsymbol{\mathrm{e}}^{−\boldsymbol{\varphi\mathrm{x}}^{\mathrm{2}} } +\boldsymbol{\mathrm{e}}^{−\boldsymbol{\delta\mathrm{x}}^{\mathrm{2}} } +\boldsymbol{\mathrm{e}}^{−\boldsymbol{\gamma\mathrm{x}}^{\mathrm{2}} } \right) \\ $$$$\boldsymbol{\gamma}−\boldsymbol{\mathrm{euler}}'\boldsymbol{\mathrm{s}}\:\boldsymbol{\mathrm{mascheroni}}\:\boldsymbol{\mathrm{constant}} \\ $$$$\boldsymbol{\varphi}−\boldsymbol{\mathrm{golden}}\:\boldsymbol{\mathrm{ratio}} \\ $$$$\boldsymbol{\delta}−\boldsymbol{\mathrm{silver}}\:\boldsymbol{\mathrm{ratio}} \\ $$$$\boldsymbol{\mathrm{klipto}}−\boldsymbol{\mathrm{quanta}}\spadesuit \\ $$
Question Number 224182 Answers: 1 Comments: 0
$$\mathrm{Calculate} \\ $$$${I}=\int\:\frac{\mathrm{sin}\:{x}}{\mathrm{1}+\:\mathrm{sin}\:{x}}\:\mathrm{d}{x} \\ $$
Question Number 224176 Answers: 2 Comments: 1
Question Number 224168 Answers: 2 Comments: 1
Question Number 224160 Answers: 0 Comments: 0
$${Q}\mathrm{224122} \\ $$
Question Number 224153 Answers: 0 Comments: 8
Question Number 224150 Answers: 0 Comments: 2
Question Number 224146 Answers: 1 Comments: 0
$$\boldsymbol{\mathrm{a}}\:=\:\mathrm{12}^{\mathrm{223}} \:\centerdot\:\mathrm{7}^{\mathrm{56}} \:+\:\mathrm{19}^{\mathrm{25}} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{last}\:\mathrm{digit}\:\mathrm{of}\:\mathrm{the}\:\mathrm{number}? \\ $$
Question Number 224144 Answers: 1 Comments: 1
Question Number 224124 Answers: 2 Comments: 0
$$\int_{−\mathrm{2}} ^{\mathrm{2}} \frac{\boldsymbol{\mathrm{x}}^{\mathrm{3}} \boldsymbol{\mathrm{cos}}\left(\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\right)+\frac{\mathrm{1}}{\mathrm{2}}}{\:\sqrt{\mathrm{4}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} }} \\ $$
Question Number 224122 Answers: 1 Comments: 1
Question Number 224121 Answers: 1 Comments: 0
Question Number 224118 Answers: 1 Comments: 0
Question Number 224113 Answers: 0 Comments: 0
$${Guys}\:{my}\:{exams}\:{are}\:{finished}\:! \\ $$$${I}\:{will}\:{be}\:{active}\:{as}\:{usual}! \\ $$$$\left.:\right) \\ $$
Question Number 224108 Answers: 3 Comments: 0
Question Number 224106 Answers: 0 Comments: 1
Question Number 224100 Answers: 1 Comments: 0
$$\mathrm{Calculate}\:\mathrm{I}=\underset{\:\mathrm{0}} {\int}^{\:+\infty} \left[\frac{\mathrm{1}}{\mathrm{t}}−\frac{\mathrm{1}}{\mathrm{sh}\left(\mathrm{t}\right)}\right]^{\:\mathrm{2}} \mathrm{dt} \\ $$
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