Question Number 60264 by maxmathsup by imad last updated on 19/May/19 $${let}\:{f}\left({t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{e}^{−\mathrm{3}\:\left[{x}^{\mathrm{2}} \right]} }{{x}^{\mathrm{2}} \:+{t}^{\mathrm{2}} }{dx}\:\:{with}\:{t}>\mathrm{0} \\ $$$$\mathrm{1}.\:{determine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({t}\right) \\ $$$$\mathrm{2}.\:{find}\:{also}\:{g}\left({t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−\mathrm{3}\left[{x}^{\mathrm{2}} \right]}…
Question Number 60263 by maxmathsup by imad last updated on 19/May/19 $${let}\:{U}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{e}^{−{n}\left[{x}^{\mathrm{2}} \right]} }{{x}^{\mathrm{2}} +\mathrm{3}}\:{dx}\: \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{U}_{{n}} \:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{n}\:{U}_{{n}} \\…
Question Number 60234 by aliesam last updated on 19/May/19 Answered by ajfour last updated on 19/May/19 $$\mathrm{z}=\mathrm{x}−\mathrm{c} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 191303 by Mingma last updated on 22/Apr/23 Answered by mahdipoor last updated on 22/Apr/23 $$\int{f}\left({x}\right)=\int{xf}^{'} \left({x}\right)−\sqrt{\mathrm{2}{x}−{x}^{\mathrm{2}} }=\left[{xf}\left({x}\right)−\int{f}\left({x}\right)\right]−\int\sqrt{\mathrm{2}{x}−{x}^{\mathrm{2}} } \\ $$$$\Rightarrow\int_{\mathrm{0}} ^{\:\mathrm{1}} {f}\left({x}\right)=\frac{\mathrm{1}}{\mathrm{2}}\left[{xf}\left({x}\right)\right]_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 125711 by TITA last updated on 13/Dec/20 $$\:\mathrm{I}=\int\frac{\mathrm{cos}\:\mathrm{2x}}{\mathrm{1}+\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}}\mathrm{dx}\:=?\:\:\mathrm{please}\:\mathrm{help} \\ $$$$ \\ $$ Answered by bramlexs22 last updated on 13/Dec/20 $${let}\:\mathrm{tan}\:\left({x}\right)=\:{t}\:\wedge\:{dt}\:=\:\frac{{dx}}{\mathrm{cos}\:^{\mathrm{2}} {x}} \\…
Question Number 60170 by necx1 last updated on 18/May/19 $$\int{x}\mathrm{sec}\:^{\mathrm{3}} {xdx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 125684 by mnjuly1970 last updated on 13/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:….\:\mathrm{INTEGRAL}… \\ $$$$\:\:\:\:\mathrm{prove}\:\:\mathrm{that}\:: \\ $$$$\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} {x}^{\mathrm{3}} \left\{{ln}\left(\mathrm{1}+{e}^{{x}} \right)\:−{x}\right\}{dx}=\frac{\mathrm{45}}{\mathrm{8}}\:\zeta\left(\:\mathrm{5}\:\right) \\ $$$$ \\ $$ Answered by Dwaipayan…
Question Number 191188 by cortano12 last updated on 20/Apr/23 $$\:\:\:\:\:\:\:\:\:\:\:\int\:\sqrt[{\mathrm{4}}]{\frac{\mathrm{2}−\mathrm{x}}{\mathrm{1}−\mathrm{x}}}\:\mathrm{dx}\:=?\: \\ $$ Answered by mehdee42 last updated on 20/Apr/23 $$\sqrt[{\mathrm{4}}]{\frac{\mathrm{2}−{x}}{\mathrm{1}−{x}}}={u}\Rightarrow{x}=\frac{{u}^{\mathrm{4}} −\mathrm{2}}{{u}^{\mathrm{4}} −\mathrm{1}}\Rightarrow{dx}=\frac{\mathrm{4}{u}^{\mathrm{3}} }{\left({u}^{\mathrm{4}} −\mathrm{1}\right)^{\mathrm{2}} \:}\:{du}…
Question Number 191142 by Mingma last updated on 19/Apr/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 60050 by maxmathsup by imad last updated on 17/May/19 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \left({x}^{\mathrm{3}} −\mathrm{2}\right)\sqrt{{x}^{\mathrm{2}} \:+\mathrm{3}}{dx} \\ $$ Commented by maxmathsup by imad last updated…