Question Number 48261 by Abdo msup. last updated on 21/Nov/18 $${let}\:{f}\left({x}\right)\:=\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{1}} \:\:\frac{{dt}}{\mathrm{2}+{ch}\left({xt}\right)} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{g}\left({x}\right)=\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{1}} \:\:\frac{{tsh}\left({xt}\right)}{\left(\mathrm{2}+{ch}\left({xt}\right)\right)^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{\mathrm{2}+{ch}\left(\mathrm{3}{t}\right)}\:{and}\:\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{1}}…
Question Number 48255 by Abdo msup. last updated on 21/Nov/18 $${calculate}\:{A}_{\lambda} \:\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left(\lambda{sinx}\right)−{sin}\left(\lambda{cosx}\right)}{{x}^{\mathrm{2}} \:+\lambda^{\mathrm{2}} }{dx} \\ $$$$\lambda\:{from}\:{R}. \\ $$ Commented by Abdo msup. last…
Question Number 48239 by olj55336@awsoo.com last updated on 21/Nov/18 $$ \\ $$$$ \\ $$$$ \\ $$$${q}…..\int\frac{{dx}}{\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}+\mathrm{2cos}\:^{\mathrm{2}} {x}},\:{please}\:{solve} \\ $$$$ \\ $$ Commented by maxmathsup by…
Question Number 113766 by Riteshgoyal last updated on 15/Sep/20 $$ \\ $$$${I}=\int_{\mathrm{0}} ^{\infty} \left(\frac{\pi}{\mathrm{1}+\pi^{\mathrm{2}} {x}^{\mathrm{2}} }−\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} }\right){lnx}\:{dx} \\ $$$${put}\:\pi{x}={tanA},\:{x}\:={tanB} \\ $$$${I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\left({ln}\left({tanA}\right)−{ln}\pi\right){dA}−\int_{\mathrm{0}} ^{\pi/\mathrm{2}} {ln}\left({tanB}\right){dB}…
Question Number 113760 by gloriousman last updated on 15/Sep/20 $$\int\sqrt{\frac{\mathrm{x}−\mathrm{1}}{\mathrm{x}^{\mathrm{5}} }}\mathrm{dx} \\ $$ Answered by bemath last updated on 15/Sep/20 $${I}=\int\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\sqrt{\frac{{x}−\mathrm{1}}{{x}}}\:{dx}\: \\ $$$${I}=\:\int\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\:\sqrt{\mathrm{1}−\frac{\mathrm{1}}{{x}}}\:{dx}\:…
Question Number 113757 by bemath last updated on 15/Sep/20 $$\:\int\:\frac{{dx}}{\mathrm{tan}\:{x}−\mathrm{sin}\:{x}}\:?\: \\ $$ Answered by bemath last updated on 15/Sep/20 Answered by Dwaipayan Shikari last updated…
Question Number 113745 by Algoritm last updated on 15/Sep/20 Answered by MJS_new last updated on 15/Sep/20 $$\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…