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Question Number 60817 Answers: 4 Comments: 2
$$\boldsymbol{\mathrm{V}}=\frac{\mathrm{4}}{\mathrm{3}}\boldsymbol{\pi\mathrm{R}}^{\mathrm{3}} \:\:\:\boldsymbol{\mathrm{prove}} \\ $$
Question Number 60816 Answers: 1 Comments: 0
$$\boldsymbol{\mathrm{S}}=\mathrm{4}\boldsymbol{\pi\mathrm{R}}^{\mathrm{2}} \:\:\:\boldsymbol{\mathrm{prove}} \\ $$
Question Number 60814 Answers: 1 Comments: 0
$${find}\:{x}\:{given}\:{that} \\ $$$$\mathrm{9}^{{sin}^{\mathrm{2}} {x}} +\mathrm{9}^{{cos}^{\mathrm{2}} {x}} =\mathrm{2}\: \\ $$$$ \\ $$
Question Number 60812 Answers: 0 Comments: 5
Question Number 60797 Answers: 0 Comments: 2
$$\int\frac{{e}^{{w}} }{{w}^{{n}+\mathrm{1}} }{dw},\:{n}\in\mathbb{N} \\ $$
Question Number 60791 Answers: 1 Comments: 2
$$\int\frac{{e}^{{n}} }{{x}^{{n}+\mathrm{1}} }{dx},\:\mathrm{n}\in\mathbb{N} \\ $$
Question Number 60788 Answers: 2 Comments: 1
Question Number 60783 Answers: 0 Comments: 2
$$\underset{ā\infty} {\overset{\infty} {\int}}{sin}\left(\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} }\right)\:{dx} \\ $$
Question Number 60775 Answers: 0 Comments: 1
Question Number 60765 Answers: 0 Comments: 2
$${express}\:{in}\:{partial}\:{fraction}\:\mathrm{14}/\left({x}^{\mathrm{2}} +\mathrm{3}\right)\left({x}+\mathrm{2}\right) \\ $$
Question Number 60756 Answers: 1 Comments: 1
$${express}\:{in}\:{partial}\:{fraction}\:\mathrm{5}/\left({x}ā\mathrm{2}\right)\left({x}+\mathrm{3}\right)^{\mathrm{2}} \\ $$
Question Number 60748 Answers: 1 Comments: 1
Question Number 60745 Answers: 4 Comments: 5
Question Number 60739 Answers: 1 Comments: 4
$${evaluate}\:\: \\ $$$${i}.\int\:\left(\frac{{x}+\mathrm{1}}{{x}ā\mathrm{1}}\right){dx} \\ $$$${ii}.\:\:\int_{\mathrm{0}} ^{\pi} \left(\mathrm{2}{cosxsinx}\right){dx}\:\: \\ $$$${iii}.\:\:\int_{\frac{\pi}{\mathrm{3}\:}\:} ^{\pi} \left(\frac{{sin}\mathrm{2}{x}}{{cos}\mathrm{2}{x}}\right){dx} \\ $$
Question Number 60735 Answers: 3 Comments: 0
$${express}\:{in}\:{partial}\:{fraction}\:\mathrm{3}/\left({x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} ā\mathrm{4}\right) \\ $$
Question Number 60734 Answers: 1 Comments: 4
$$\mathrm{Find}\:\mathrm{the}\:\mathrm{product}\:\mathrm{of}\:\mathrm{the}\:\mathrm{real}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\:\:\:\:\:\:\:\:\:\left(\mathrm{x}\:+\:\mathrm{2}\:+\:\sqrt{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{4x}\:+\:\mathrm{3}}\right)^{\mathrm{5}} \:ā\:\:\mathrm{32}\left(\mathrm{x}\:+\:\mathrm{2}\:ā\:\sqrt{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{4x}\:+\:\mathrm{3}}\right)^{\mathrm{5}} \:\:=\:\:\mathrm{31} \\ $$
Question Number 60731 Answers: 0 Comments: 0
Question Number 60728 Answers: 0 Comments: 0
$${calculate}\:\int_{\mathrm{1}} ^{+\infty} \:\:\frac{{ln}\left({lnx}\right)}{{x}^{\mathrm{2}} ā{x}\:+\mathrm{1}}{dx} \\ $$
Question Number 60727 Answers: 0 Comments: 2
$${calculate}\:\int_{\mathrm{1}} ^{+\infty} \:\frac{{ln}\left({lnx}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$
Question Number 60725 Answers: 0 Comments: 2
$${x}\:\:=\:\:\underset{\mathrm{0}\leqslant{i}\leqslant{j}\leqslant\mathrm{2019}} {\sum}\:\left(\:_{\:\:\:\:{j}} ^{\mathrm{2019}} \:\right)\left(\:\:_{{i}} ^{{j}} \:\:\right)\: \\ $$
Question Number 60723 Answers: 0 Comments: 8
$${solve}\:{for}\:{x}\: \\ $$$$\sqrt{{a}ā\sqrt{{a}+{x}}}\:+\:\sqrt{{a}+\sqrt{{a}ā{x}}}\:=\:\mathrm{2}{x} \\ $$
Question Number 60717 Answers: 0 Comments: 1
Question Number 60706 Answers: 0 Comments: 2
$${let}\:{f}\left({x}\right)\:=\sqrt{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$$$\left.\mathrm{1}\right)\:{let}\:{U}_{{n}} ={f}^{\left({n}\right)} \left({x}\right)\:\:{prove}\:{that}\:\sum_{{k}=\mathrm{0}} ^{{n}} \:{C}_{{n}} ^{{k}} \:{U}_{{k}} {U}_{{n}+\mathrm{1}ā{k}} =\mathrm{0}\:\:{for}\:{n}\geqslant\mathrm{2} \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}\:. \\ $$
Question Number 60705 Answers: 1 Comments: 0
Question Number 60716 Answers: 1 Comments: 1
Question Number 60702 Answers: 0 Comments: 0
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