Question Number 44179 by abdo.msup.com last updated on 22/Sep/18 $$\left.\mathrm{1}\right)\:{find}\:\int\:\:\:\frac{{dx}}{\:\sqrt{{x}^{\mathrm{2}} \:+{x}+\mathrm{1}}+\sqrt{{x}^{\mathrm{2}} −{x}+\mathrm{1}}} \\ $$$$\left.\mathrm{2}\right){calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\:\frac{{dx}}{\:\sqrt{{x}^{\mathrm{2}} \:+{x}+\mathrm{1}}+\sqrt{{x}^{\mathrm{2}} −{x}\:+\mathrm{1}}} \\ $$ Commented by maxmathsup by imad…
Question Number 44178 by abdo.msup.com last updated on 22/Sep/18 $${find}\:\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\pi} \:\:\frac{{sin}^{\mathrm{2}} {t}}{\left({x}^{\mathrm{2}} −\mathrm{2}{x}\:{cost}\:+\mathrm{1}\right)^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{{sin}^{\mathrm{2}} {t}}{\left({x}^{\mathrm{2}} −{cost}\:+\mathrm{1}\right)^{\mathrm{2}} }{dt} \\ $$ Terms…
Question Number 44175 by abdo.msup.com last updated on 22/Sep/18 $${find}\:\:{f}\left({a}\right)\:=\int_{\mathrm{1}} ^{+\infty} \:\:\frac{{dx}}{{ch}^{\mathrm{2}} {x}\:+{a}\:{sh}^{\mathrm{2}} {x}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{1}} ^{+\infty} \:\:\:\frac{{dx}}{{ch}^{\mathrm{2}} {x}+\mathrm{2}{sh}^{\mathrm{2}} {x}} \\ $$ Commented by maxmathsup…
Question Number 44176 by abdo.msup.com last updated on 22/Sep/18 $${find}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \left({t}^{{n}} −\left[{t}\right]\right){e}^{−{nt}} {dt} \\ $$$${and}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$$${n}\:{integr}\:{natural}. \\ $$ Commented by abdo.msup.com…
Question Number 175244 by infinityaction last updated on 24/Aug/22 $$\:{prove}\:{that} \\ $$$$\:\int_{\mathrm{0}} ^{{a}} \int_{\mathrm{0}} ^{\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{2}} }} \frac{{dx}\:{dy}}{\left(\mathrm{1}+{e}^{{y}} \right)\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{2}} −{y}^{\mathrm{2}} }}\:=\:\frac{\pi}{\mathrm{2}}\mathrm{log}\:\frac{\mathrm{2}{e}^{{a}} }{\mathrm{1}+{e}^{{a}} } \\…
Question Number 175247 by rexford last updated on 24/Aug/22 Answered by Ar Brandon last updated on 24/Aug/22 $${I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{sin}^{\mathrm{2}} \mathrm{4}\vartheta\mathrm{cos}^{\mathrm{5}} \mathrm{4}\vartheta{d}\vartheta \\ $$$$\:\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…
Question Number 44174 by abdo.msup.com last updated on 22/Sep/18 $${find}\:\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}\:{e}^{{i}\theta} \right)} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 109709 by nimnim last updated on 25/Aug/20 $$\:\:\:\:\:\int_{\mathrm{0}\:} ^{\frac{\pi}{\mathrm{4}}} \mathrm{ln}\left(\mathrm{tanx}+\mathrm{1}\right)\mathrm{dx} \\ $$ Answered by mnjuly1970 last updated on 25/Aug/20 $$\mathrm{I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left(\mathrm{1}+{tanx}\right){dx}\overset{\int_{{a}} ^{\:{b}}…
Question Number 44173 by abdo.msup.com last updated on 22/Sep/18 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dt}}{\left(\mathrm{3}+{t}^{\mathrm{2}} \right)\sqrt{\mathrm{1}+{t}}}{dt} \\ $$ Commented by maxmathsup by imad last updated on 23/Sep/18 $${let}\:{I}\:=\int_{\mathrm{0}}…
Question Number 44148 by LXZ last updated on 22/Sep/18 $$\int{dx}/{sinx}\centerdot{sin}\left({x}+\alpha\right)=? \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 22/Sep/18 $$\int\frac{{dx}}{{sinx}.{sin}\left({x}+\alpha\right)} \\ $$$$\frac{\mathrm{1}}{{sin}\alpha}\int\frac{{sin}\left\{\left({x}+\alpha\right)−{x}\right\}}{{sinx}.{sin}\left({x}+\alpha\right)}{dx} \\ $$$$\frac{\mathrm{1}}{{sin}\alpha}\int\frac{{sin}\left({x}+\alpha\right){cosx}−{cos}\left({x}+\alpha\right){sinx}}{{sinxsin}\left({x}+\alpha\right)}{dx} \\…