Question Number 207099 by tri26112004 last updated on 06/May/24 Answered by Berbere last updated on 06/May/24 $$=\int_{−\infty} ^{\infty} \frac{{e}^{{i}\pi{ax}} }{\left({x}^{\mathrm{2}} +\beta^{\mathrm{2}} \right)^{{n}+\mathrm{1}} }{dx};{a}\in\mathbb{R}_{+} \\ $$$${if}\:{Imx}\geqslant\mathrm{0}\:\mid{e}^{{i}\pi{ax}}…
Question Number 207054 by Ghisom last updated on 05/May/24 $$\Omega_{\alpha} =\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{x}^{\alpha} \sqrt{−{x}\mathrm{ln}\:{x}}\:{dx}=? \\ $$ Answered by Frix last updated on 05/May/24 $$\alpha>−\frac{\mathrm{3}}{\mathrm{2}} \\…
Question Number 206962 by Ghisom last updated on 01/May/24 $$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\frac{\sqrt{\mathrm{1}−{x}}}{\:\sqrt{\mathrm{1}−\sqrt{\mathrm{1}−{x}}}+\sqrt{\mathrm{1}+\sqrt{\mathrm{1}−{x}}}}{dx}=? \\ $$ Answered by lepuissantcedricjunior last updated on 02/May/24 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\sqrt{\mathrm{1}−\boldsymbol{{x}}}}{\:\sqrt{\mathrm{1}−\sqrt{\mathrm{1}−\boldsymbol{{x}}}}+\sqrt{\mathrm{1}+\sqrt{\mathrm{1}−\boldsymbol{{x}}}}}\boldsymbol{{dx}}=\boldsymbol{{k}} \\…
Question Number 206892 by mathzup last updated on 29/Apr/24 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{dx} \\ $$ Answered by Frix last updated on 29/Apr/24 $${t}={x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}} \\…
Question Number 206890 by mathzup last updated on 29/Apr/24 $${can}\:{some}\:{one}\:{find}\:{the}\:{exact}\:{value}\:{of} \\ $$$$\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}}{\left({n}!\right)^{\mathrm{2}} } \\ $$ Commented by Frix last updated on 30/Apr/24 $$\mathrm{This}\:\mathrm{is}\:\mathrm{a}\:\mathrm{Modified}\:\mathrm{Bressel}\:\mathrm{Function}\:\mathrm{of}\:\mathrm{the}…
Question Number 206830 by Fabricista15 last updated on 27/Apr/24 $${c}\:=\:\sqrt{\left(\int_{{a}_{\mathrm{0}} } ^{{a}_{\mathrm{1}} } \sqrt{\mathrm{1}+\left[{f}'\left({x}\right)\right]^{\mathrm{2}} }{dx}\right)^{\mathrm{2}} +\left(\int_{{b}_{\mathrm{0}} } ^{{b}_{\mathrm{1}} } \sqrt{\mathrm{1}+\left[{f}'\left({x}\right)\right]^{\mathrm{2}} }{dx}\right)^{\mathrm{2}} } \\ $$$${c}\:=\:\sqrt{{L}_{\mathrm{1}} ^{\mathrm{2}}…
Question Number 206829 by 2kdw last updated on 27/Apr/24 $$\:\:\:\:\:\oint\frac{{x}}{{x}+\mathrm{2}}{dx}^{\mathrm{2}} \:\:\:\:{is}\:{wrong}? \\ $$ Commented by mr W last updated on 27/Apr/24 $${there}\:{are}\:{things}\:{to}\:{which}\:{you}\:{can} \\ $$$${say}\:{they}\:{are}\:{wrong},\:{for}\:{example} \\…
Question Number 206858 by Ghisom last updated on 27/Apr/24 $$\mathrm{prove}\:\mathrm{that} \\ $$$${H}_{{n}} =\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{{t}^{{n}} −\mathrm{1}}{{t}−\mathrm{1}}{dt} \\ $$ Answered by mathzup last updated on 28/Apr/24…
Question Number 206789 by BaliramKumar last updated on 25/Apr/24 Answered by A5T last updated on 25/Apr/24 $$\sqrt[{{n}}]{{a}_{\mathrm{1}} {a}_{\mathrm{2}} …{a}_{{n}} }={P} \\ $$$$\sqrt[{\mathrm{2}{n}}]{{a}_{{n}+\mathrm{1}} {a}_{{n}+\mathrm{2}} …{a}_{\mathrm{3}{n}} }={Q}…
Question Number 206791 by akolade last updated on 25/Apr/24 $$\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−\sqrt{\mathrm{x}}}.\mathrm{ln}^{\mathrm{2}} \mathrm{x}\:\mathrm{dx} \\ $$ Commented by Frix last updated on 25/Apr/24 $$\mathrm{Question}\:\mathrm{206754} \\ $$…