Question Number 50423 by Abdo msup. last updated on 16/Dec/18 $${find}\:{f}\left({a}\right)\:=\int_{{a}} ^{+\infty} \:\:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\sqrt{{x}^{\mathrm{2}} −{a}^{\mathrm{2}} }}\:\:{with}\:{a}>\mathrm{0} \\ $$ Commented by Abdo msup. last updated on…
Question Number 50422 by Abdo msup. last updated on 16/Dec/18 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{ln}\left({x}\right)}{\:\sqrt{{x}}\left(\mathrm{1}−{x}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} }{dx} \\ $$ Commented by Abdo msup. last updated on 23/Dec/18 $${changement}\:{x}\:={sin}^{\mathrm{2}}…
Question Number 50421 by Abdo msup. last updated on 16/Dec/18 $${calculate}\:{A}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{3}}} \:\:\:\:\frac{{du}}{\left(\mathrm{1}+{cos}^{\mathrm{2}} {u}\right)^{\mathrm{3}} } \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 50420 by Abdo msup. last updated on 16/Dec/18 $${find}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{6}}} \:\:{cosx}\:{ln}\left({cosx}\right){dx} \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 17/Dec/18 $${let}\:{I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{6}}} {cosxln}\left({cosx}\right){dx}…
Question Number 50417 by Abdo msup. last updated on 16/Dec/18 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{arctan}\sqrt{\mathrm{1}−\frac{{x}^{\mathrm{2}} }{\mathrm{2}}}{dx} \\ $$ Commented by Abdo msup. last updated on 19/Dec/18 $${changement}\:{x}=\sqrt{\mathrm{2}}{sin}\theta\:{give}…
Question Number 50418 by Abdo msup. last updated on 16/Dec/18 $${calculate}\:\int_{\mathrm{0}} ^{{lln}\left(\mathrm{3}\right)} \:\:\frac{{sh}^{\mathrm{2}} \left({x}\right){dx}}{{ch}^{\mathrm{3}} \left({x}\right)} \\ $$ Commented by Abdo msup. last updated on 24/Dec/18…
Question Number 50416 by Abdo msup. last updated on 16/Dec/18 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:^{\mathrm{3}} \sqrt{{x}^{\mathrm{2}} \left(\mathrm{1}−{x}^{\mathrm{3}} \right)}{dx} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 17/Dec/18…
Question Number 50415 by Abdo msup. last updated on 16/Dec/18 $${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{dt}}{\mathrm{1}+{cos}\theta\:{cost}} \\ $$ Commented by Abdo msup. last updated on 18/Dec/18 $${let}\:{put}\:{cos}\theta\:=\:\lambda\:{and}\:{find}\:{A}\left(\lambda\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…
Question Number 50413 by Abdo msup. last updated on 16/Dec/18 $${let}\:{f}\:\in{C}^{\mathrm{0}} \left({R},{R}\right)\:/\:\forall\:{x}\in{R}\:\:{f}\left({a}+{b}−{x}\right)={f}\left({x}\right) \\ $$$$\left.\mathrm{1}\right)\:{find}\:\int_{{a}} ^{{b}} {xf}\left({x}\right){dx}\:{interms}\:{of}\:\int_{{a}} ^{{b}} {f}\left({x}\right){dx} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{{xdx}}{\mathrm{1}+{sinx}} \\ $$ Commented…
Question Number 50414 by Abdo msup. last updated on 16/Dec/18 $${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{x}\:{sinx}\:{cosx}}{{tan}^{\mathrm{2}} {x}\:+{cotan}^{\mathrm{2}} {x}}{dx} \\ $$$${ctanx}\:=\frac{\mathrm{1}}{{tanx}} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on…