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Question Number 136167 by ZiYangLee last updated on 19/Mar/21 $$\mathrm{Given}\:\mathrm{that}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{value}\:\mathrm{for}\:\mathrm{the}\:\mathrm{5}^{\mathrm{th}} \\ $$$$\mathrm{root}\:\mathrm{of}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{number}\:\mathrm{is}\:−\mathrm{1}+{i}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{another}\:\mathrm{four}\:\mathrm{values}. \\ $$ Answered by mr W last updated on 19/Mar/21 $${one}\:\mathrm{5}^{{th}}…

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Question Number 5048 by LMTV last updated on 05/Apr/16 $$\int\left({x}\sqrt{{x}}+\mathrm{1}\right)^{\mathrm{2}} {dx}=? \\ $$$$\int{y}\left(\mathrm{2}{y}+\mathrm{1}\right)^{\mathrm{2}} {dy}=? \\ $$$$\int\frac{\mathrm{1}}{\mathrm{4sec}\:{x}}{dx}=? \\ $$$${y}=\mathrm{sec}^{\mathrm{3}} \:\left(\mathrm{2}{x}+\mathrm{5}\right) \\ $$$${y}'=? \\ $$ Commented by…

Question Number 136098 by SOMEDAVONG last updated on 18/Mar/21 $$\left.\mathrm{I}\right).\mathrm{compute}\:\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{1000}} {\sum}}\mathrm{C}_{\mathrm{2000}} ^{\mathrm{2k}} . \\ $$ Answered by Olaf last updated on 18/Mar/21 $$\left(\mathrm{1}−\mathrm{1}\right)^{\mathrm{2000}} \:=\:\mathrm{0}\:=\:\underset{{p}=\mathrm{0}}…

Question Number 5011 by Yozzii last updated on 01/Apr/16 Commented by Yozzii last updated on 01/Apr/16 $${S}=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{1}}{{ln}\left({n}\right)}\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{{tan}^{−\mathrm{1}} {i}}{{n}−{i}+\mathrm{1}}\right) \\ $$$${S}=?\: \\ $$…