Question Number 48289 by Abdulhafeez Abu qatada last updated on 21/Nov/18 $${Evaluate}\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\frac{{Log}\left({x}\right)}{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{3}}\:{dx} \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 22/Nov/18 Commented…
Question Number 113821 by 675480065 last updated on 15/Sep/20 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{ln}\left(\mathrm{2}−\mathrm{sinx}\right)\mathrm{dx} \\ $$ Commented by Dwaipayan Shikari last updated on 15/Sep/20 $${I}\left({a}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {log}\left(\mathrm{2}+{asinx}\right){dx}…
Question Number 179344 by neinhaltsieger369 last updated on 28/Oct/22 $$\: \\ $$$$\:\mathrm{Help}-\mathrm{me}! \\ $$$$\: \\ $$$$\:\int_{\mathrm{0}} ^{\:\boldsymbol{\pi}} \int_{\mathrm{0}} ^{\:\mathrm{3}\boldsymbol{\mathrm{cos}}\:\boldsymbol{\phi}} \boldsymbol{\theta\mathrm{sin}}\:\boldsymbol{\phi\mathrm{d}\theta\mathrm{d}\phi} \\ $$$$\: \\ $$ Commented…
Question Number 48264 by Abdo msup. last updated on 21/Nov/18 $${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{sin}\left(\mathrm{2}{t}\right)}{\mathrm{1}+{x}\:{cos}\left({t}\right)}{dt} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{also}\:{g}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\frac{{sin}\left(\mathrm{2}{t}\right){cost}}{\left(\mathrm{1}+{xcost}\right)^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{3}\right){find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{sin}\left(\mathrm{2}{t}\right)}{\mathrm{1}+\mathrm{3}\:{cos}\left({t}\right)}{dt}\:{and} \\…
Question Number 48261 by Abdo msup. last updated on 21/Nov/18 $${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…