Question Number 200684 by Spillover last updated on 21/Nov/23 $$\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\int_{−\mathrm{4}\pi} ^{\mathrm{4}\pi} \:\:\:\frac{\mid{x}\mid\:\mathrm{sin}\:^{\mathrm{2}{n}} {x}}{\mathrm{sin}\:^{\mathrm{2}{n}} {x}+\mathrm{cos}\:^{\mathrm{2}{n}} {x}}{dx} \\ $$$$ \\ $$$$ \\ $$ Answered by…
Question Number 200685 by Spillover last updated on 21/Nov/23 $$\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \mathrm{ln}\:\left(\mathrm{1}+\mathrm{tan}{x}\right){dx}\: \\ $$$$ \\ $$ Answered by som(math1967) last updated on 22/Nov/23…
Question Number 200622 by sonukgindia last updated on 21/Nov/23 Answered by Rasheed.Sindhi last updated on 21/Nov/23 $$\bullet\left({a}+{b}+{c}\right)^{\mathrm{2}} =\mathrm{4}^{\mathrm{2}} =\mathrm{16} \\ $$$$\:\:\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} +\mathrm{2}\left({ab}+{bc}+{ca}\right)=\mathrm{16} \\…
Question Number 200617 by sonukgindia last updated on 21/Nov/23 Answered by Frix last updated on 21/Nov/23 $${x}+{a}={y}^{\mathrm{2}} \\ $$$${y}+{a}={x}^{\mathrm{2}} \\ $$$${x}−{y}={y}^{\mathrm{2}} −{x}^{\mathrm{2}} \\ $$$${x}^{\mathrm{2}} −{y}^{\mathrm{2}}…
Question Number 200618 by sonukgindia last updated on 21/Nov/23 Commented by Frix last updated on 21/Nov/23 $$\sqrt{\mathrm{2}}−\mathrm{1} \\ $$ Answered by Rasheed.Sindhi last updated on…
Question Number 200619 by sonukgindia last updated on 21/Nov/23 Answered by witcher3 last updated on 21/Nov/23 $$\mathrm{I}_{\mathrm{9}} =\mathrm{2}\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{x}^{\mathrm{a}} }{\mathrm{c}+\mathrm{kx}^{\mathrm{b}} }\mathrm{dx} \\ $$$$\mathrm{in}\:\infty\:\mathrm{c}+\mathrm{kx}^{\mathrm{b}} \sim\mathrm{x}^{\mathrm{b}}…
Question Number 200677 by a.lgnaoui last updated on 21/Nov/23 $$\int\frac{\mathrm{df}}{\mathrm{dx}}×\frac{\mathrm{dg}}{\mathrm{dx}}\:\:\:\:\:? \\ $$ Commented by mr W last updated on 22/Nov/23 $${it}'{s}\:{just}\:{non}−{sense}. \\ $$ Terms of…
Question Number 200657 by cherokeesay last updated on 21/Nov/23 Answered by Frix last updated on 21/Nov/23 $$\mathrm{3}\sqrt[{\mathrm{4}}]{\mathrm{27}{x}^{\mathrm{2}} +\mathrm{24}{x}+\frac{\mathrm{28}}{\mathrm{3}}}=\mathrm{4}+\sqrt[{\mathrm{3}}]{\frac{\mathrm{81}{x}}{\mathrm{2}}−\mathrm{1}} \\ $$$$\mathrm{3}\sqrt[{\mathrm{4}}]{\frac{\mathrm{81}{x}^{\mathrm{2}} +\mathrm{72}{x}+\mathrm{28}}{\mathrm{3}}}=\mathrm{4}+\sqrt[{\mathrm{3}}]{\frac{\mathrm{81}{x}−\mathrm{2}}{\mathrm{2}}} \\ $$$${x}=\frac{{t}}{\mathrm{9}} \\ $$$$\mathrm{3}\sqrt[{\mathrm{4}}]{\frac{{t}^{\mathrm{2}}…
Question Number 200646 by Calculusboy last updated on 21/Nov/23 Answered by Frix last updated on 21/Nov/23 $$\left(\frac{\mathrm{1}+\mathrm{sin}\:\theta\:+\mathrm{i}\:\mathrm{cos}\:\theta}{\mathrm{1}+\mathrm{sin}\:\theta\:−\mathrm{i}\:\mathrm{cos}\:\theta}\right)^{{n}} =\left(\mathrm{sin}\:\theta\:+\mathrm{i}\:\mathrm{cos}\:\theta\right)^{{n}} = \\ $$$$=\left(\mathrm{cos}\:\left(\frac{\pi}{\mathrm{2}}−\theta\right)\:+\mathrm{i}\:\mathrm{sin}\:\left(\frac{\pi}{\mathrm{2}}−\theta\right)\right)^{{n}} =\mathrm{e}^{\mathrm{i}\left(\frac{\pi}{\mathrm{2}}−\theta\right){n}} = \\ $$$$=\mathrm{cos}\:\left(\left(\frac{\pi}{\mathrm{2}}−\theta\right){n}\right)\:+\mathrm{i}\:\mathrm{sin}\:\left(\left(\frac{\pi}{\mathrm{2}}−\theta\right){n}\right)…
Question Number 200574 by Harnada last updated on 20/Nov/23 $${sorry}\:{mr}\:{W} \\ $$ Commented by mr W last updated on 20/Nov/23 $${for}\:{what}? \\ $$ Commented by…