Question Number 66695 by mathmax by abdo last updated on 18/Aug/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({arctanx}\right)}{\mathrm{4}+{x}^{\mathrm{2}} }{dx} \\ $$ Commented by ~ À ® @ 237 ~…
Question Number 66694 by mathmax by abdo last updated on 18/Aug/19 $$\left.{let}\:{f}\left({a}\right)\:=\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{4}} +{x}^{\mathrm{2}} \:+{a}\right)}\:{with}\:{a}\in\right]\frac{\mathrm{1}}{\mathrm{4}},+\infty\left[\right. \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{also}\:{g}\left({a}\right)\:=\int_{−\infty} ^{+\infty} \:\frac{{dx}}{\left({x}^{\mathrm{4}} \:+{x}^{\mathrm{2}} +{a}\right)^{\mathrm{2}} }…
Question Number 66693 by mathmax by abdo last updated on 18/Aug/19 $${calculate}\:\:\int_{−\infty} ^{+\infty} \:\frac{{dx}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)^{\mathrm{3}} } \\ $$ Commented by mathmax by abdo last updated…
Question Number 132192 by benjo_mathlover last updated on 12/Feb/21 $$\:\int\:\frac{\mathrm{dx}}{\mathrm{csc}\:\mathrm{x}\:+\:\mathrm{sec}\:\mathrm{x}} \\ $$ Answered by Dwaipayan Shikari last updated on 12/Feb/21 $$\int\frac{{sinx}\:{cosx}}{{sinx}+{cosx}}{dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int{sinx}+{cosx}−\frac{\mathrm{1}}{{sinx}+{cosx}}{dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\left({sinx}−{cosx}\right)−\int\frac{{dt}}{\mathrm{1}−{t}^{\mathrm{2}}…
Question Number 1124 by 123456 last updated on 17/Jun/15 $$\mathrm{lets}\:{f}:\left[\mathrm{0},\mathrm{1}\right]\rightarrow\mathbb{R}\:\mathrm{given}\:\mathrm{by} \\ $$$${f}\left({x}\right)=\begin{cases}{{x}}&{{x}\in\mathbb{Q}}\\{\mathrm{1}−{x}}&{{x}\notin\mathbb{Q}}\end{cases} \\ $$$$\mathrm{is}\:{f}\:\mathrm{continuos}\:\mathrm{at}\:{x}=\mathrm{1}/\mathrm{2}? \\ $$$$\mathrm{is}\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{fdx}\:\mathrm{riemann}\:\mathrm{integrable}? \\ $$$$\mathrm{is}\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{fdx}\:\mathrm{lebesgue}\:\mathrm{integable}? \\ $$ Commented…
Question Number 132191 by rs4089 last updated on 12/Feb/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{log}_{{e}} \left({x}+\mathrm{1}\right)}{{x}\left({x}^{\mathrm{2}} +\mathrm{1}\right)}{dx} \\ $$ Answered by mathmax by abdo last updated on 12/Feb/21…
Question Number 66627 by behi83417@gmail.com last updated on 17/Aug/19 Commented by behi83417@gmail.com last updated on 17/Aug/19 $$\mathrm{reposted}!\:\:\mathrm{Q}#\mathrm{62227} \\ $$ Commented by mathmax by abdo last…
Question Number 1085 by 123456 last updated on 10/Jun/15 $$\mathrm{I}=\underset{\mathrm{0}} {\overset{\pi} {\int}}\frac{{x}\left(\pi−{x}\right)}{\mathrm{sin}\:{x}}{dx} \\ $$ Commented by 123456 last updated on 10/Jun/15 $${f}\left({x}\right)=\frac{{x}\left(\pi−{x}\right)}{\mathrm{sin}\:{x}} \\ $$$${f}\left(\mathrm{0}^{+} \right)\overset{?}…
Question Number 66589 by Tanmay chaudhury last updated on 17/Aug/19 $$\int\frac{{sinx}}{\mathrm{1}+{sinx}+{sin}\mathrm{2}{x}}{dx} \\ $$ Commented by MJS last updated on 17/Aug/19 $$\mathrm{Weierstrass}\:\left[{t}=\mathrm{tan}\:\frac{{x}}{\mathrm{2}}\:\rightarrow\:{dx}=\frac{\mathrm{2}{dt}}{{t}^{\mathrm{2}} +\mathrm{1}}\right]\:\mathrm{leads}\:\mathrm{to} \\ $$$$\mathrm{4}\int\frac{{t}}{\left({t}+\mathrm{1}\right)\left({t}^{\mathrm{3}} −\mathrm{3}{t}^{\mathrm{2}}…
Question Number 132121 by abdullahquwatan last updated on 11/Feb/21 $$\int_{\mathrm{2}} ^{\mathrm{8}} \frac{\sqrt{{x}}}{\:\sqrt{\mathrm{10}−{x}}\:+\sqrt{{x}}}\:\mathrm{dx} \\ $$ Commented by Dwaipayan Shikari last updated on 11/Feb/21 $$\mathrm{3} \\ $$…