Question Number 535 by kth last updated on 25/Jan/15 $$\int_{\mathrm{4}} ^{\mathrm{1}} \frac{\mathrm{2}}{\:\sqrt{{x}}} \\ $$ Answered by 13/NaSaNa(N)056565 last updated on 25/Jan/15 $$=\mathrm{2}\int_{\mathrm{4}} ^{\mathrm{1}} {x}^{\frac{−\mathrm{1}}{\mathrm{2}}} {dx}…
Question Number 66064 by mathmax by abdo last updated on 08/Aug/19 $${find}\:{the}\:{value}\:{of}\:\int_{−\infty} ^{+\infty} \:{cos}\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right){dx} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 131602 by rs4089 last updated on 06/Feb/21 Answered by mnjuly1970 last updated on 06/Feb/21 $$\frac{\zeta\left(\mathrm{3}\right)}{\mathrm{8}} \\ $$ Answered by mathmax by abdo last…
Question Number 66062 by mathmax by abdo last updated on 08/Aug/19 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{{ch}\left({t}\right)+{xsh}\left({t}\right)} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{dt}}{\left({ch}\left({t}\right)+{xsh}\left({t}\right)\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{{ch}\left({t}\right)+\mathrm{3}{sh}\left({t}\right)}\:{and}\:\int_{\mathrm{0}}…
Question Number 66065 by mathmax by abdo last updated on 08/Aug/19 $${find}\:{the}\:{value}\:{of}\:{U}_{{n}} =\int_{−\infty} ^{+\infty} {e}^{−{nx}^{\mathrm{2}} } {sin}\left({x}^{\mathrm{2}} −\mathrm{2}{x}\right){dx} \\ $$$${find}\:{nature}\:{of}\:{the}\:{serie}\:\Sigma\:{U}_{{n}} \:{and}\:\Sigma{e}^{−{n}^{\mathrm{2}} } {U}_{{n}} \\ $$…
Question Number 66060 by mathmax by abdo last updated on 08/Aug/19 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{dt}}{{x}+{tant}}\:\:{with}\:{x}\:{real} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{aexplicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{also}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{dt}}{\left({x}+{tant}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right){give}\:{f}^{\left({n}\right)} \left({x}\right){at}\:{form}\:{of}\:{integral} \\…
Question Number 66048 by aliesam last updated on 08/Aug/19 $$\int\frac{{x}}{\:\sqrt{{ln}\left(\mathrm{1}/{x}\right)}}\:{dx} \\ $$ Commented by Prithwish sen last updated on 08/Aug/19 $$\int\frac{\mathrm{x}}{\:\sqrt{−\mathrm{lnx}}}\mathrm{dx}\:\:\:\mathrm{put}−\mathrm{lnx}\:=\:\mathrm{u}^{\mathrm{2}} \:\Rightarrow\mathrm{dx}=−\mathrm{2ue}^{−\mathrm{u}^{\mathrm{2}} } \\ $$$$=\:−\mathrm{2}\int\mathrm{e}^{−\mathrm{2u}^{\mathrm{2}}…
Question Number 131581 by mnjuly1970 last updated on 06/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:…\:{nice}\:\:\:\:\:{calculus}… \\ $$$$\:\:\:{evaluate}\::: \\ $$$$\:\Omega=\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({x}\right)}{{x}}{ln}\left(\frac{{a}+{cos}^{\mathrm{2}} \left({x}\right)}{{b}+{cos}^{\mathrm{2}} \left({x}\right)}\right){dx}=? \\ $$$$ \\ $$ Commented…
Question Number 66044 by rajesh4661kumar@gmail.com last updated on 08/Aug/19 Answered by Tanmay chaudhury last updated on 08/Aug/19 $$\int\frac{{dx}}{{x}^{\mathrm{5}} \left(\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{4}} }\right)^{\frac{\mathrm{3}}{\mathrm{4}}} } \\ $$$${t}=\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{4}} }\rightarrow{dt}=\frac{−\mathrm{4}}{{x}^{\mathrm{5}} }{dx}…
Question Number 509 by kth last updated on 25/Jan/15 $$\int{f}\left({x}\right){dx} \\ $$ Answered by 123456 last updated on 21/Jan/15 $${F}\left({x}\right)+{C} \\ $$ Terms of Service…