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Question Number 84767 Answers: 1 Comments: 0
$${Find}\:\:{all}\:\:{solutions}\:\:{of} \\ $$$$\:\:\:\:\:\:\:\mathrm{2020}{x}^{\mathrm{2}} \:−\:{y}^{\mathrm{2}} \:\:=\:\:\mathrm{6059} \\ $$$${x},\:{y}\:<\:\:\mathrm{2020}\:\:,\:\:\:{x},\:{y}\:\:\in\:\:\mathbb{N} \\ $$
Question Number 84766 Answers: 1 Comments: 2
$$\int\:\frac{\mathrm{dx}}{\left(\mathrm{16}+\mathrm{9sin}\:\mathrm{x}\right)^{\mathrm{2}} } \\ $$$$ \\ $$
Question Number 84759 Answers: 1 Comments: 0
$${calculate}\:\:\int_{−\infty} ^{+\infty} \:\:\frac{{arctan}\left(\mathrm{2}{x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$
Question Number 84740 Answers: 1 Comments: 5
$$\mathrm{find}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{when}\:−\mathrm{18}\:\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{4} \\ $$
Question Number 84739 Answers: 1 Comments: 0
$$\mathrm{find}\:\mathrm{the}\:\mathrm{unit}\:\mathrm{digit}\:\mathrm{in}\:\mathrm{the}\:\mathrm{number} \\ $$$$\:\mathrm{15}^{\mathrm{1789}} \:+\:\mathrm{17}^{\mathrm{1789}} \:+\:\mathrm{19}^{\mathrm{1789}} \\ $$
Question Number 84733 Answers: 1 Comments: 0
$$\int\frac{{x}^{\mathrm{4}} +\mathrm{1}}{{x}^{\mathrm{6}} +\mathrm{1}}{dx} \\ $$
Question Number 84728 Answers: 0 Comments: 8
$${y}={x}\left[{x}\left[{x}\right]\right]\:{with}\:{x}\in{R}^{+} \\ $$$${find}\:{the}\:{range}\:{of}\:{function} \\ $$$${and}\:{solve}\:{x}\left[{x}\left[{x}\right]\right]=\mathrm{150}. \\ $$
Question Number 84726 Answers: 0 Comments: 0
$${prove}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \left({y}^{{y}} \right)^{\left({y}^{{y}} \right)^{\left({y}^{{y}} \right)^{.^{.^{.} } } } } {dy}=\frac{\pi^{\mathrm{2}} }{\mathrm{12}} \\ $$
Question Number 84718 Answers: 2 Comments: 0
Question Number 84785 Answers: 1 Comments: 2
$$\mathrm{at}\:\mathrm{what}\:\mathrm{time}\:\mathrm{is}\:\mathrm{the}\:\mathrm{short}\:\mathrm{clock}\: \\ $$$$\mathrm{and}\:\mathrm{long}\:\mathrm{hour}\:\mathrm{hand}\:\mathrm{form}\:\mathrm{an}\: \\ $$$$\mathrm{angle}\:\mathrm{of}\:\mathrm{180}\:\mathrm{degrees}? \\ $$
Question Number 84713 Answers: 2 Comments: 2
$$\int\overset{\:\:\mathrm{1}} {\:}_{\mathrm{0}} \mathrm{cos}^{−\mathrm{1}} \left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}\right)\:\mathrm{dx}\:? \\ $$
Question Number 84711 Answers: 0 Comments: 2
Question Number 84702 Answers: 0 Comments: 3
Question Number 84709 Answers: 1 Comments: 0
$$\int\sqrt[{\mathrm{3}}]{{tan}\left({x}\right)}\:{dx} \\ $$
Question Number 84708 Answers: 1 Comments: 0
Question Number 84693 Answers: 1 Comments: 1
Question Number 84689 Answers: 1 Comments: 2
Question Number 84685 Answers: 0 Comments: 0
$$\int\frac{{dx}}{{x}\left(\mathrm{2}−{e}^{{x}} \right)} \\ $$
Question Number 84683 Answers: 1 Comments: 0
$${x}\in{N}\:{and}\:{y}\in{N}:\left({x}<{y}\right) \\ $$$${slove}\:\left({E}\right): \\ $$$${xy}−\mathrm{4}{y}+\mathrm{3}{x}−\mathrm{2027}=\mathrm{0}.....\left({E}\right) \\ $$
Question Number 84682 Answers: 0 Comments: 5
Question Number 84681 Answers: 1 Comments: 1
Question Number 84680 Answers: 1 Comments: 0
$${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \frac{{log}\left({xyz}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{y}^{\mathrm{2}} \right)\left(\mathrm{1}+{z}^{\mathrm{2}} \right)}\:{dx}\:{dy}\:{dz}=\frac{−\mathrm{3}\pi^{\mathrm{2}} {G}}{\mathrm{16}} \\ $$
Question Number 84677 Answers: 0 Comments: 1
$$\underset{\mathrm{k}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{k}^{\mathrm{2}} }{\mathrm{2}^{\mathrm{k}} }\:?\: \\ $$
Question Number 84667 Answers: 0 Comments: 1
Question Number 84666 Answers: 1 Comments: 2
$$\int\:{x}\:\mathrm{sin}^{−\mathrm{1}} \left({x}\right)\:{dx}\: \\ $$
Question Number 84674 Answers: 0 Comments: 1
$$\frac{\mathrm{6}−\mathrm{log}_{\mathrm{16}} \:\left(\mathrm{x}^{\mathrm{4}} \right)}{\mathrm{3}+\mathrm{2log}_{\mathrm{16}} \left(\mathrm{x}^{\mathrm{2}} \right)}\:<\:\mathrm{2} \\ $$
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