Question Number 113336 by 175mohamed last updated on 12/Sep/20 $${If}\:\mathrm{1},\:{a}^{\mathrm{2}} ,{a}^{\mathrm{3}} \:,…,{a}^{{n}−\mathrm{1}} \:{are}\:{the}\:{roots}\: \\ $$$${nth}\:{of}\:{unity}\:,\: \\ $$$${prove}\:{that}\::\:\left(\mathrm{1}+{a}\right)\left(\mathrm{1}+{a}^{\mathrm{2}} \right)\left(\mathrm{1}+{a}^{\mathrm{3}} \right)…\left(\mathrm{1}+{a}^{{n}−\mathrm{1}} \right) \\ $$$$=\:{n}−\mathrm{2}\lfloor\frac{{n}}{\mathrm{2}}\rfloor \\ $$$$ \\…
Question Number 47770 by tanmay.chaudhury50@gmail.com last updated on 14/Nov/18 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{\mathrm{2}} −\mathrm{1}}{{lnx}}{dx} \\ $$ Commented by maxmathsup by imad last updated on 14/Nov/18 $${you}\:{are}\:{welcome}\:{sir}.…
Question Number 47771 by tanmay.chaudhury50@gmail.com last updated on 14/Nov/18 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{x}}{{tanx}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 178822 by Mastermind last updated on 21/Oct/22 Answered by Rasheed.Sindhi last updated on 22/Oct/22 $$\left.\mathrm{24}\right) \\ $$$$\frac{\mathrm{1}/\mathrm{4}+{x}+\mathrm{1}/\mathrm{6}}{\mathrm{3}}=\frac{\mathrm{1}}{\mathrm{4}} \\ $$$${x}+\frac{\mathrm{3}+\mathrm{2}}{\mathrm{12}}=\frac{\mathrm{3}}{\mathrm{4}} \\ $$$${x}=\frac{\mathrm{3}}{\mathrm{4}}−\frac{\mathrm{5}}{\mathrm{12}}=\frac{\mathrm{9}−\mathrm{5}}{\mathrm{12}}=\frac{\mathrm{1}}{\mathrm{3}} \\ $$…
Question Number 47743 by tanmay.chaudhury50@gmail.com last updated on 14/Nov/18 $$\int\frac{{dx}}{{x}^{{n}} −{x}}\:\: \\ $$$${the}\:{problems}\:{i}\:{have}\:{posted}\:{are}\:{tricky}… \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 14/Nov/18 $$\int\frac{{dx}}{{x}\left({x}^{{n}−\mathrm{1}} −\mathrm{1}\right)} \\…
Question Number 47740 by tanmay.chaudhury50@gmail.com last updated on 14/Nov/18 $$\int\frac{{dx}}{{x}\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\left({x}+\mathrm{3}\right)…\left({x}+{n}\right)} \\ $$ Answered by ajfour last updated on 14/Nov/18 $$\frac{\mathrm{1}}{{x}\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)…\left({x}+{r}\right)…\left({x}+{n}\right)} \\ $$$$=\:\Sigma\frac{{A}_{{r}} }{{x}+{r}}\: \\ $$$${A}_{{r}}…
Question Number 178785 by Mastermind last updated on 21/Oct/22 Answered by Rasheed.Sindhi last updated on 21/Oct/22 $$ \\ $$$$\sqrt[{\mathrm{4}}]{\frac{\mathrm{3}−{x}}{\mathrm{3}+{x}}}\:−\sqrt{\frac{\mathrm{3}+{x}}{\mathrm{3}−{x}}}\:=\sqrt{\mathrm{2}} \\ $$$${Let}\:\sqrt[{\mathrm{4}}]{\frac{\mathrm{3}−{x}}{\mathrm{3}+{x}}}\:={y} \\ $$$$\:\:\:\:\:\:\:\:\sqrt{\frac{\mathrm{3}−{x}}{\mathrm{3}+{x}}}\:={y}^{\mathrm{2}} \Rightarrow\sqrt{\frac{\mathrm{3}+{x}}{\mathrm{3}−{x}}}\:=\frac{\mathrm{1}}{{y}^{\mathrm{2}} }…
Question Number 178787 by ali009 last updated on 21/Oct/22 $${use}\:{convolution}\:{theorm}\:{to}\:{find}\:{y}\left({t}\right) \\ $$$${if}\:{Y}\left({s}\right)=\frac{\mathrm{5}}{\left({s}^{\mathrm{2}} +\mathrm{1}\right)\left({s}^{\mathrm{2}} +\mathrm{25}\right)} \\ $$ Commented by aleks041103 last updated on 21/Oct/22 $${is}\:{Y}\left({s}\right)\:{the}\:{laplace}\:{tranform}\:{of}\:{y}\left({t}\right)? \\…
Question Number 113190 by Dwaipayan Shikari last updated on 11/Sep/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{logx}}{{x}−\mathrm{1}}{dx} \\ $$ Commented by Dwaipayan Shikari last updated on 11/Sep/20 $$−\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 113185 by 175mohamed last updated on 11/Sep/20 Answered by mindispower last updated on 12/Sep/20 $${z}^{{n}} −\mathrm{1}=\underset{{k}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\prod}}\left({z}−{a}_{{k}} \right) \\ $$$${z}=−\mathrm{1}\Rightarrow\left(−\mathrm{1}\right)^{{n}} −\mathrm{1}=\underset{{k}=\mathrm{0}} {\overset{{n}−\mathrm{1}}…