Question Number 130387 by Bird last updated on 25/Jan/21 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{cos}\left({abx}\right)}{\left({x}^{\mathrm{2}} +{ax}+\mathrm{1}\right)\left({x}^{\mathrm{2}} +{bx}+\mathrm{1}\right)} \\ $$$${with}\:{a}\:{and}\:{b}\:{real}\:{and}\:\mid{a}\mid<\mathrm{2},\mid{b}\mid<\mathrm{2} \\ $$ Commented by mathmax by abdo last updated…
Question Number 64850 by mathmax by abdo last updated on 22/Jul/19 $${let}\:{A}_{\lambda} \:=\int_{\mathrm{0}} ^{\pi} \:\:\:\frac{{dx}}{\lambda\:\:+{cosx}\:+{sinx}}\:\:\:\:\left(\lambda\:\in\:{R}\right) \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{A}_{\lambda} \\ $$$$\left.\mathrm{2}\right)\:\:{find}\:{also}\:{B}_{\lambda} \:=\int_{\mathrm{0}} ^{\pi} \:\:\frac{{dx}}{\left(\lambda\:+{cosx}\:+{sinx}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}}…
Question Number 64818 by mathmax by abdo last updated on 22/Jul/19 $${find}\:\int\:\:\:\frac{{dx}}{\mathrm{1}+{cosx}\:+{cos}\left(\mathrm{2}{x}\right)} \\ $$ Commented by mathmax by abdo last updated on 22/Jul/19 $${let}\:{I}\:=\int\:\frac{{dx}}{\mathrm{1}+{cosx}\:+{cos}\left(\mathrm{2}{x}\right)}\:\Rightarrow\:{I}\:=\int\:\frac{{dx}}{\mathrm{1}+{cosx}+\mathrm{2}{cos}^{\mathrm{2}} {x}−\mathrm{1}}…
Question Number 64805 by mmkkmm000m last updated on 21/Jul/19 $$\int{log}\frac{\left(\mathrm{1}+{sinhx}\right)}{\left(\mathrm{1}−{sinhx}\right)}{tanhx}\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 64801 by mmkkmm000m last updated on 21/Jul/19 $$\int\left({cos}^{\mathrm{4}} {x}+{sin}^{\mathrm{4}} {x}\right)/\left({cos}\mathrm{2}{x}+\mathrm{1}\right){dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 64802 by mmkkmm000m last updated on 21/Jul/19 $$\int\left({cos}^{\mathrm{4}} {x}+{sin}^{\mathrm{4}} {x}\right)/\left({cos}\mathrm{2}{x}+\mathrm{1}\right){dx} \\ $$ Commented by mathmax by abdo last updated on 22/Jul/19 $${let}\:{I}\:=\int\:\:\frac{{cos}^{\mathrm{4}} {x}+{sin}^{\mathrm{4}}…
Question Number 130326 by rs4089 last updated on 24/Jan/21 Answered by Lordose last updated on 24/Jan/21 $$ \\ $$$$\Omega\left(\mathrm{p}\right)\:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{sin}\left(\mathrm{px}\right)}{\mathrm{x}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)}\mathrm{dx} \\ $$$$\Omega'\left(\mathrm{p}\right)\:=\:\int_{\mathrm{0}} ^{\:\infty}…
Question Number 130320 by benjo_mathlover last updated on 24/Jan/21 $$\:\int\:\frac{\mathrm{x}−\mathrm{1}}{\left(\mathrm{x}−\mathrm{2}\right)\left(\mathrm{x}^{\mathrm{2}} −\mathrm{2x}+\mathrm{2}\right)^{\mathrm{2}} }\:\mathrm{dx}\: \\ $$ Answered by EDWIN88 last updated on 24/Jan/21 $$\mathrm{Let}\:\mathcal{E}\:=\:\int\:\frac{{x}−\mathrm{1}}{\left({x}−\mathrm{2}\right)\left({x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{2}\right)^{\mathrm{2}} }\:{dx} \\…
Question Number 130306 by benjo_mathlover last updated on 24/Jan/21 $$\int_{\mathrm{0}} ^{\:\infty} \:\mathrm{x}\:\mathrm{cos}\:\left(\mathrm{x}\right)\:\mathrm{ln}\:\left(\mathrm{x}\right)\mathrm{e}^{−\mathrm{x}} \:\mathrm{dx}\:?\: \\ $$ Answered by Dwaipayan Shikari last updated on 24/Jan/21 $${I}\left({a}\right)=\int_{\mathrm{0}} ^{\infty}…
Question Number 64762 by Lontum Hans-Sandys last updated on 21/Jul/19 $$\mathrm{Given}\:\mathrm{that}\:\mathrm{g}\left(\mathrm{x}\right)=\frac{\mathrm{2}}{\left(\mathrm{1}+\mathrm{x}\right)\left(\mathrm{1}+\mathrm{3x}^{\mathrm{2}} \right.} \\ $$$$\left.\mathrm{a}\right)\:\mathrm{express}\:\mathrm{g}\left(\mathrm{x}\right)\:\mathrm{in}\:\mathrm{partial}\:\mathrm{fractions}. \\ $$$$\left.\mathrm{b}\right)\:\mathrm{evaluate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{g}\left(\left(\mathrm{x}\right)\:\mathrm{dx}.\right. \\ $$ Commented by mathmax by abdo…