Question Number 113745 by Algoritm last updated on 15/Sep/20 Answered by MJS_new last updated on 15/Sep/20 $$\frac{\mathrm{2cos}\:\mathrm{2}{x}\:−\mathrm{cos}\:{x}}{\mathrm{6}−\mathrm{cos}^{\mathrm{2}} \:{x}\:−\mathrm{4sin}\:{x}}= \\ $$$$=−\frac{\mathrm{cos}\:{x}}{\mathrm{sin}^{\mathrm{2}} \:{x}\:−\mathrm{4sin}\:{x}\:+\mathrm{5}}+\frac{\mathrm{2}\left(\mathrm{2cos}^{\mathrm{2}} \:{x}\:−\mathrm{1}\right)}{\mathrm{sin}^{\mathrm{2}} \:{x}\:−\mathrm{4sin}\:{x}\:+\mathrm{5}} \\ $$$$…
Question Number 113738 by bemath last updated on 15/Sep/20 $$\:\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\frac{{x}\:\mathrm{sin}\:{x}}{\mathrm{1}+\mathrm{cos}\:^{\mathrm{2}} {x}}\:{dx}\:? \\ $$ Answered by bobhans last updated on 15/Sep/20 $$\mathrm{I}\:=\:\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\frac{\mathrm{x}\:\mathrm{sin}\:\mathrm{x}}{\mathrm{1}+\mathrm{cos}\:^{\mathrm{2}}…
Question Number 48182 by cesar.marval.larez@gmail.com last updated on 20/Nov/18 Answered by tanmay.chaudhury50@gmail.com last updated on 20/Nov/18 $$\left.\mathrm{1}\right){t}=\frac{{x}^{{m}} {y}^{{n}} }{\left({x}+{y}\right)^{{m}+{n}} } \\ $$$${lnt}={mlnx}+{nlny}−\left({m}+{n}\right){ln}\left({x}+{y}\right) \\ $$$$\frac{\mathrm{1}}{{t}}\frac{{dt}}{{dx}}=\frac{{m}}{{x}}+\frac{{n}}{{y}}×\frac{{dy}}{{dx}}−\frac{{m}+{n}}{{x}+{y}}\left(\mathrm{1}+\frac{{dy}}{{dx}}\right) \\…
Question Number 48177 by Abdo msup. last updated on 20/Nov/18 $${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\int_{{x}+\mathrm{1}} ^{\mathrm{2}{x}+\mathrm{1}} \:\:\:\frac{{tarctan}\left({t}^{\mathrm{2}} +\mathrm{1}\right)}{\mathrm{1}+\left(\mathrm{1}+{t}^{\mathrm{2}} \right)^{\mathrm{2}} }{dt} \\ $$ Commented by kaivan.ahmadi last updated on…
Question Number 48178 by Abdo msup. last updated on 20/Nov/18 $${find}\:\:\int\:\:\:\frac{{sin}\left(\pi{x}\right)}{\mathrm{3}\:+{cos}\left(\mathrm{2}\pi{x}\right)}{dx} \\ $$ Commented by Abdo msup. last updated on 25/Nov/18 $${A}=\int\:\:\:\frac{{sin}\left(\pi{x}\right)}{\mathrm{3}+{cos}\left(\mathrm{2}\pi{x}\right)}{dx}\:=_{\pi{x}\:={t}} \:\:\frac{\mathrm{1}}{\pi}\int\:\:\:\frac{{sin}\left({t}\right)}{\mathrm{3}+{cos}\left(\mathrm{2}{t}\right)}{dt} \\ $$$$\:\int\:\:\:\frac{{sin}\left({t}\right)}{\mathrm{3}\:+\mathrm{2}{cos}^{\mathrm{2}}…
Question Number 48175 by Abdo msup. last updated on 20/Nov/18 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\int_{{x}} ^{{x}^{\mathrm{2}} } \:\:\:\frac{{ln}\left(\mathrm{1}+{t}\right)}{{sin}\left({t}\right)}{dt} \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 179244 by Acem last updated on 27/Oct/22 $${Evaluate}\:\int\mathrm{tan}^{\mathrm{4}} \:{x}\:\mathrm{sec}^{\mathrm{5}} \:{x}\:{dx} \\ $$ Answered by ARUNG_Brandon_MBU last updated on 27/Oct/22 $${I}=\int\mathrm{tan}^{\mathrm{4}} {x}\mathrm{sec}^{\mathrm{5}} {xdx}=\int\mathrm{tan}^{\mathrm{3}} {x}\mathrm{sec}^{\mathrm{4}}…
Question Number 48173 by Abdo msup. last updated on 20/Nov/18 $${calculate}\:\int\:\:\frac{{arctan}\left({x}\right)}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{dx} \\ $$ Commented by maxmathsup by imad last updated on 26/Nov/18 $${changement}\:{x}={tant}\:{give}\:\:{I}\:=\:\int\:\frac{{t}}{\:\sqrt{\mathrm{1}+{tan}^{\mathrm{2}} {t}}}\:\left(\mathrm{1}+{tan}^{\mathrm{2}}…
Question Number 48172 by Abdo msup. last updated on 20/Nov/18 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{sin}\left(\mathrm{2}{cos}\left({x}^{\mathrm{2}} +\mathrm{1}\right)\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$ Commented by Abdo msup. last updated on 25/Nov/18…
Question Number 48170 by Abdo msup. last updated on 20/Nov/18 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{cos}\left({sin}\left({x}^{\mathrm{2}} \right)\right)}{\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} }{dx} \\ $$ Commented by maxmathsup by imad last updated on…