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AllQuestion and Answers: Page 1259
Question Number 85839 Answers: 1 Comments: 1
$$\int\mathrm{x}×\frac{\mathrm{1}}{\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}}\mathrm{dx} \\ $$
Question Number 85835 Answers: 1 Comments: 0
$$\mathrm{xydy}=\left(\mathrm{y}^{\mathrm{2}} +\mathrm{x}\right)\mathrm{dx} \\ $$
Question Number 85834 Answers: 1 Comments: 0
$$\mathrm{2y}^{'} −\frac{\mathrm{x}}{\mathrm{y}}=\frac{\mathrm{xy}}{\mathrm{x}^{\mathrm{2}} −\mathrm{1}} \\ $$
Question Number 85832 Answers: 1 Comments: 1
$$\left(\mathrm{x}+\mathrm{x}^{−\mathrm{1}} \right)^{\mathrm{2}} +\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}^{−\mathrm{2}} \right)^{\mathrm{2}} +\left(\mathrm{x}^{\mathrm{3}} +\mathrm{x}^{−\mathrm{3}} \right)^{\mathrm{2}} \\ $$$$+\:...\:+\:\left(\mathrm{x}^{\mathrm{10}} +\mathrm{x}^{−\mathrm{10}} \right)^{\mathrm{2}} \:=\: \\ $$
Question Number 85828 Answers: 1 Comments: 0
$$\int\frac{\mathrm{1}}{{x}+{cot}\left({x}\right)}\:{dx} \\ $$
Question Number 85826 Answers: 1 Comments: 2
$$\:^{\mathrm{x}} \mathrm{log}\:\left(\mathrm{xy}\right).\:^{\mathrm{y}} \mathrm{log}\:\left(\mathrm{xy}\right)\:+\:^{\mathrm{x}} \mathrm{log}\:\left(\mathrm{x}−\mathrm{y}\right).^{\mathrm{y}} \mathrm{log}\:\left(\mathrm{x}−\mathrm{y}\right)=\mathrm{0} \\ $$$$\mathrm{find}\:\mathrm{x}+\mathrm{y}\: \\ $$
Question Number 85822 Answers: 2 Comments: 1
$$\mathrm{how}\:\mathrm{to}\:\mathrm{solve}\: \\ $$$$\sqrt[{\mathrm{3}\:\:}]{\mathrm{x}−\mathrm{1}}\:+\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{x}−\mathrm{3}}\:+\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{x}−\mathrm{5}}\:=\:\mathrm{0}\: \\ $$
Question Number 85817 Answers: 2 Comments: 0
$$\mathrm{what}\:\mathrm{is}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{x}^{\mathrm{2}} \:\mathrm{in}\: \\ $$$$\mathrm{the}\:\mathrm{expansion}\:\left[\:\left(\mathrm{1}−\mathrm{x}\right)\left(\mathrm{1}+\mathrm{2x}\right)\right]^{\mathrm{6}} \\ $$
Question Number 85807 Answers: 1 Comments: 0
$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\mathrm{x}^{\mathrm{2}} \:\mathrm{dx}}{\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{4}} }} \\ $$
Question Number 85801 Answers: 0 Comments: 3
$${calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{{dx}}{\left({cosx}\:+\mathrm{2}{sinx}\right)^{\mathrm{2}} } \\ $$
Question Number 85793 Answers: 0 Comments: 0
$$\int_{\mathrm{1}} ^{\mathrm{2}} \frac{{tan}^{−\mathrm{1}} \left({x}−\mathrm{1}\right)\:{ln}\left({x}−\mathrm{1}\right)}{{x}}\:{dx} \\ $$
Question Number 85789 Answers: 1 Comments: 0
$$\int\left(\mathrm{ln}\:{x}\right)^{\mathrm{2}} \:{dx}\:= \\ $$
Question Number 85786 Answers: 0 Comments: 0
$${posons}\: \\ $$$$\left(\mathrm{1}+\mathrm{2}\sqrt{\mathrm{3}}\right)^{\boldsymbol{{n}}} =\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} +\boldsymbol{\mathrm{b}}_{\boldsymbol{\mathrm{n}}} \sqrt{\mathrm{3}} \\ $$$$\boldsymbol{\mathrm{montre}}\:\boldsymbol{\mathrm{que}}\:\boldsymbol{\mathrm{pgcd}}\left(\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} ;\boldsymbol{{b}}_{\boldsymbol{{n}}} \right)=\mathrm{1} \\ $$
Question Number 85781 Answers: 1 Comments: 2
$$\int_{\mathrm{0}} ^{\mathrm{1}} \:\left(\mathrm{ln}\:\frac{\mathrm{1}}{{x}}\right)^{−\mathrm{3}/\mathrm{2}} \:{dx} \\ $$
Question Number 85779 Answers: 0 Comments: 0
Question Number 85776 Answers: 1 Comments: 0
Question Number 85775 Answers: 0 Comments: 0
Question Number 85774 Answers: 0 Comments: 0
$$\left({x}_{\mathrm{2}{n}} \right)=\mathrm{2}^{\mathrm{2}{n}} \left(\frac{{x}}{\mathrm{2}}\right)_{{n}} \left(\frac{{x}+\mathrm{1}}{\mathrm{2}}\right)_{{n}} \\ $$$$\left({x}\right)_{{m}\:{n}} ={m}^{{m}\:{n}} \underset{{k}=\mathrm{0}} {\overset{{m}=\mathrm{1}} {\prod}}\left(\frac{{x}+{k}}{{m}}\right)_{{n}} \:\:\:,\:{m}\in{z} \\ $$$${now}\:{if}\:{m}\:{is}\:{relative}\:{number}\:{such}\:{as}\frac{\mathrm{3}}{\mathrm{2}}\:,\:{m}\in{Q} \\ $$$$\left({x}\right)_{\frac{\mathrm{3}}{\mathrm{2}}{n}} =?? \\ $$$$ \\ $$$${help}\:{me}\: \\ $$
Question Number 85766 Answers: 0 Comments: 2
$$\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{1}−\mathrm{sin}\:\left(\mathrm{x}+\mathrm{2y}\right) \\ $$
Question Number 85762 Answers: 0 Comments: 12
Question Number 85760 Answers: 0 Comments: 0
$$\int\frac{\left[{cos}^{−\mathrm{1}} \left({x}\right)\left\{\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\right\}\right]^{−\mathrm{1}} }{{log}\left\{\frac{{sin}\left(\mathrm{2}{x}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\right)}{\pi}\right\}}\:{dx} \\ $$
Question Number 85756 Answers: 0 Comments: 5
Question Number 85739 Answers: 1 Comments: 0
$$\mathrm{If}\:{F}\:\left({x}\right)=\underset{{x}^{\mathrm{2}} } {\overset{{x}^{\mathrm{3}} } {\int}}\:\mathrm{log}\:{t}\:{dt}\:\:\left({x}>\mathrm{0}\right),\:\mathrm{then}\:{F}\:'\left({x}\right)= \\ $$
Question Number 85729 Answers: 0 Comments: 6
$$\mathrm{if}\:\mathrm{march}\:\mathrm{24},\:\mathrm{2020}\:\mathrm{is}\:\mathrm{Tuesday}, \\ $$$$\mathrm{then}\:\mathrm{march}\:\mathrm{24},\:\mathrm{2032}\:\mathrm{is}\:\mathrm{the}\:\mathrm{day}\:? \\ $$
Question Number 85721 Answers: 1 Comments: 0
$${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{{e}^{−{x}} {ln}\left({x}\right)}{\sqrt{{x}}}{dx}=−\sqrt{\pi}\left(\gamma+{ln}\left(\mathrm{4}\right)\right) \\ $$
Question Number 85718 Answers: 1 Comments: 0
$$\int\frac{{sin}\left({x}\right)−{cos}\left(\mathrm{3}{x}\right)}{{sin}\left({x}\right)−{cos}\left(\mathrm{2}{x}\right)}{dx} \\ $$
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