Question Number 126349 by mnjuly1970 last updated on 19/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:\:\:\:\:{calculate}\:::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Omega\overset{???} {=}\int_{\mathrm{0}} ^{\:\:\infty} {e}^{\:−{t}} \:{t}^{\:\mathrm{2}} \:{j}_{\mathrm{0}} \left(\:{t}\:\right){dt} \\ $$$$\:\:\:\:\:{where}\::\:\:{j}_{\left({v}\right)} \left({x}\right)={x}^{{v}} \underset{{n}=\mathrm{0}} {\overset{\:\infty}…
Question Number 126344 by mnjuly1970 last updated on 19/Dec/20 $$\:\:\:\:\: \\ $$$$\:\:\:{evaluate}\:::\:\:\:\int_{−\mathrm{1}} ^{\:\:\mathrm{0}} \frac{{dx}}{\:\sqrt[{\mathrm{3}}]{\mathrm{1}+{x}^{\mathrm{3}} }}\:=? \\ $$$$ \\ $$ Answered by Dwaipayan Shikari last updated…
Question Number 60797 by arcana last updated on 25/May/19 $$\int\frac{{e}^{{w}} }{{w}^{{n}+\mathrm{1}} }{dw},\:{n}\in\mathbb{N} \\ $$ Commented by MJS last updated on 26/May/19 $$\mathrm{this}\:\mathrm{reminds}\:\mathrm{me}\:\mathrm{of}\:\Gamma\left({x}\right)=\underset{\mathrm{0}} {\overset{\infty} {\int}}\mathrm{e}^{−{t}} {t}^{{x}−\mathrm{1}}…
Question Number 60791 by arcana last updated on 25/May/19 $$\int\frac{{e}^{{n}} }{{x}^{{n}+\mathrm{1}} }{dx},\:\mathrm{n}\in\mathbb{N} \\ $$ Commented by Forkum Michael Choungong last updated on 25/May/19 $$\int\frac{{e}^{{n}} }{{x}^{{n}+\mathrm{1}}…
Question Number 126323 by mnjuly1970 last updated on 19/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{advanced}\:\:{calculus}… \\ $$$$\:\:\:\:\:{prove}\:\:\:{that}\:::: \\ $$$$\:\:\:\:\:\frac{\Gamma\left(\frac{\mathrm{1}−{x}}{\mathrm{2}}\right)\Gamma\left({x}\right)}{\Gamma\left(\frac{{x}}{\mathrm{2}}\right)}\:\overset{???} {=}\:\frac{\mathrm{2}^{{x}−\mathrm{1}} \sqrt{\pi}}{{cos}\left(\frac{\pi{x}}{\mathrm{2}}\right)} \\ $$$$ \\ $$ Terms of Service Privacy Policy…
Question Number 60783 by aliesam last updated on 25/May/19 $$\underset{−\infty} {\overset{\infty} {\int}}{sin}\left(\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} }\right)\:{dx} \\ $$ Commented by maxmathsup by imad last updated on 25/May/19 $${let}\:{A}\:=\int_{−\infty}…
Question Number 126316 by benjo_mathlover last updated on 19/Dec/20 $$\:\:\underset{\:\sqrt{\mathrm{2}}} {\overset{\mathrm{2}{e}^{\sqrt{\mathrm{2}}} } {\int}}\mathrm{ln}\:\left(\frac{{e}^{{x}} +{e}^{−{x}} }{\mathrm{9}\sqrt{{x}}}\right){dx}\:?\: \\ $$ Commented by liberty last updated on 19/Dec/20 $$\int\:\left(\mathrm{ln}\left(\:{e}^{{x}}…
Question Number 126315 by MathSh last updated on 19/Dec/20 $$\int\frac{\mathrm{1}}{{dx}}=? \\ $$ Answered by Olaf last updated on 19/Dec/20 $$\mathrm{No}\:\mathrm{mathematical}\:\mathrm{meaning}. \\ $$ Terms of Service…
Question Number 126314 by benjo_mathlover last updated on 19/Dec/20 $$\:\:\int\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\:? \\ $$ Answered by Dwaipayan Shikari last updated on 19/Dec/20 $$\int\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\:\:\:\:\:\:\:\:{x}={sin}\theta…
Question Number 126298 by bramlexs22 last updated on 19/Dec/20 $$\:\:\int_{\:\mathrm{0}} ^{\:\sqrt{\mathrm{ln}\:\left(\pi/\mathrm{2}\right)}} {xe}^{{x}^{\mathrm{2}} } \mathrm{sin}\:\left({e}^{{x}^{\mathrm{2}} } \right)\:{dx}\:? \\ $$ Answered by liberty last updated on 19/Dec/20…