Question Number 119939 by huotpat last updated on 28/Oct/20 Answered by bramlexs22 last updated on 28/Oct/20 $$\:\int\:\frac{\left(\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}} {x}\right)\:\mathrm{cos}\:{x}\:{dx}\:}{\mathrm{1}−\mathrm{2sin}\:{x}} \\ $$$$\:\left[\:{let}\:\mathrm{sin}\:{x}\:=\:{s}\:\right] \\ $$$$\int\:\frac{\left(\mathrm{1}−{s}^{\mathrm{2}} \right){ds}}{\mathrm{1}−\mathrm{2}{s}}\:=\:\int\:\frac{{s}^{\mathrm{2}} −\mathrm{1}}{\mathrm{2}{s}−\mathrm{1}}\:{ds} \\…
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Question Number 119921 by bramlexs22 last updated on 28/Oct/20 $${solving}\:{the}\:{following}\:{system}\:{of}\:{equations} \\ $$$$\begin{cases}{\frac{\mathrm{3}{x}−{y}}{{x}−\mathrm{3}{y}}={x}^{\mathrm{2}} }\\{\frac{\mathrm{3}{y}−{z}}{{y}−\mathrm{3}{z}}={y}^{\mathrm{2}} }\\{\frac{\mathrm{3}{z}−{x}}{{z}−\mathrm{3}{x}}={z}^{\mathrm{2}} }\end{cases} \\ $$ Answered by mindispower last updated on 28/Oct/20 $$\Rightarrow{x}=\frac{{z}^{\mathrm{3}}…
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Question Number 119894 by danielasebhofoh last updated on 27/Oct/20 Answered by mathmax by abdo last updated on 28/Oct/20 $$\:\:\mathrm{let}\:\mathrm{I}_{\mathrm{n}} =\int\:\frac{\mathrm{dx}}{\mathrm{x}\left(\mathrm{x}^{\mathrm{n}} −\mathrm{a}^{\mathrm{n}} \right)}\:\:\mathrm{if}\:\mathrm{a}\neq\mathrm{0}\:\mathrm{we}\:\mathrm{do}\:\mathrm{the}\:\mathrm{changement}\:\mathrm{x}=\mathrm{at}\:\Rightarrow \\ $$$$\mathrm{I}_{\mathrm{n}} =\int\:\frac{\mathrm{adt}}{\mathrm{at}\left(\mathrm{a}^{\mathrm{n}}…
Question Number 185414 by Safiullah_21 last updated on 21/Jan/23 $$\mathrm{2}^{{x}} ={a} \\ $$$$\mathrm{3}^{{y}} ={b}\:\:\:\:\:\::\:\mathrm{6}^{{xy}} =? \\ $$$$\Rightarrow\mathrm{6}^{{xy}} =\left(\mathrm{2}×\mathrm{3}\right)^{{xy}} \Rightarrow\mathrm{2}^{{xy}} ×\mathrm{3}^{{xy}} \Rightarrow\left(\mathrm{2}^{{x}} \right)^{{y}} ×\left(\mathrm{3}^{{y}} \right)^{{x}} \Rightarrow{a}^{{y}}…
Question Number 185403 by mathlove last updated on 21/Jan/23 $$\underset{{k}=\mathrm{1}} {\overset{\mathrm{16}} {\sum}}\left(\sqrt{{k}}−\sqrt{{k}−\mathrm{1}}\right)=? \\ $$ Answered by aba last updated on 21/Jan/23 $$=\mathrm{4} \\ $$ Answered…
Question Number 185395 by mathlove last updated on 21/Jan/23 Answered by witcher3 last updated on 21/Jan/23 $$\mathrm{x}^{\mathrm{4}} +\frac{\mathrm{1}}{\mathrm{4}}=\left(\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\frac{\mathrm{1}}{\mathrm{2}}\right)\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\frac{\mathrm{1}}{\mathrm{2}}\right) \\ $$$$\left(\mathrm{2k}+\mathrm{1}\right)^{\mathrm{2}} −\left(\mathrm{2k}+\mathrm{1}\right)+\frac{\mathrm{1}}{\mathrm{2}}=\left(\mathrm{2k}\right)^{\mathrm{2}} +\mathrm{2k}+\frac{\mathrm{1}}{\mathrm{2}} \\…
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Question Number 185394 by mathlove last updated on 21/Jan/23 Answered by mr W last updated on 21/Jan/23 $${P}×\left(\mathrm{3}^{\mathrm{2}^{\mathrm{0}} } −\mathrm{1}\right)=\left(\mathrm{3}^{\mathrm{2}^{\mathrm{1}} } −\mathrm{1}\right)\left(\mathrm{3}^{\mathrm{2}^{\mathrm{1}} } +\mathrm{1}\right)…\left(\mathrm{3}^{\mathrm{2}^{{n}} }…