Question Number 64873 by mathmax by abdo last updated on 22/Jul/19 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\pi} \:\:\frac{{dt}}{{x}+{sint}}\:\:\:{with}\:{xreal} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{also}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\pi} \:\:\frac{{dt}}{\left({x}+{sint}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:{give}\:{f}^{\left({n}\right)} \left({x}\right)\:{at}\:{form}\:{of}\:{integral} \\…
Question Number 130402 by pipin last updated on 25/Jan/21 $$\: \\ $$$$\:\int\:\left(\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{x}}} \right).\left(\frac{\boldsymbol{\mathrm{x}}^{\mathrm{6}} +\boldsymbol{\mathrm{x}}^{\mathrm{5}} +\mathrm{5}\boldsymbol{\mathrm{x}}^{\mathrm{4}} }{\left(\mathrm{1}+\boldsymbol{\mathrm{x}}\right)^{\mathrm{6}} }\right)\boldsymbol{\mathrm{dx}}\:=\:… \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 64866 by mathmax by abdo last updated on 22/Jul/19 $${find}\:\int_{\mathrm{1}} ^{+\infty} \:\frac{{dx}}{{x}^{\mathrm{2}} \sqrt{\mathrm{1}+{x}+{x}^{\mathrm{2}} }} \\ $$ Commented by mathmax by abdo last updated…
Question Number 130392 by mathmax by abdo last updated on 25/Jan/21 $$\mathrm{find}\:\int_{\mid\mathrm{z}\mid=\mathrm{1}} \:\:\frac{\mathrm{1}−\mathrm{cosz}}{\mathrm{z}^{\mathrm{2}} }\mathrm{dz} \\ $$ Answered by mohammad17 last updated on 25/Jan/21 $${hello}\:{sir}\:{can}\:{you}\:{help}\:{me}\:{in}\:{Q}\:\mathrm{130416} \\…
Question Number 130390 by mathmax by abdo last updated on 25/Jan/21 $$\mathrm{find}\:\int_{\mid\mathrm{z}\mid=\mathrm{1}} \:\:\:\frac{\mathrm{z}^{\mathrm{2}} }{\mathrm{3}+\mathrm{sinz}}\mathrm{dz} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 130391 by mathmax by abdo last updated on 25/Jan/21 $$\mathrm{calculate}\:\int_{\mid\mathrm{z}\mid=\mathrm{1}} \:\:\:\frac{\mathrm{tanz}}{\mathrm{z}}\mathrm{dz} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 130389 by mathmax by abdo last updated on 25/Jan/21 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{z}\right)=\frac{\mathrm{1}}{\mathrm{1}−\mathrm{cos}\left(\mathrm{2z}\right)}\:\mathrm{determine}\:\mathrm{Res}\left(\mathrm{f},\mathrm{o}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 130387 by Bird last updated on 25/Jan/21 $${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}}…