Question Number 142362 by mnjuly1970 last updated on 30/May/21 $$ \\ $$$$\:\:\:\:\:\:\:\:\:{prove}\:\:{that}: \\ $$$$\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} {ln}\left(\frac{\mathrm{1}}{{x}}\right).{j}_{\mathrm{0}} \left({x}\right){dx}:=\:\gamma+{ln}\left(\mathrm{2}\right)\: \\ $$$$\:\:\:\:\:{Hint}:\left(\mathrm{1}\right) \\ $$$$\:\:\:\:\:\:\:{j}_{\mathrm{0}} \left({x}\right)=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} {x}^{\mathrm{2}{n}}…
Question Number 76826 by Master last updated on 30/Dec/19 Answered by john santu last updated on 31/Dec/19 $$=\:\int\underset{\mathrm{0}} {\overset{\mathrm{2}} {\:}}\:\int\underset{\mathrm{0}} {\overset{\:\mathrm{1}} {\:}}\:\int\underset{\mathrm{0}} {\overset{\:\mathrm{3}} {\:}}\:\left(\mathrm{2}{y}+{z}+{x}\right)\:{dz}\:{dy}\:{dx}\: \\…
Question Number 142358 by rs4089 last updated on 30/May/21 $$\int_{\mathrm{0}} ^{\infty} {x}^{{n}−\mathrm{1}} {log}_{{e}} \left(\mathrm{1}−{x}\right){dx} \\ $$ Answered by mathmax by abdo last updated on 30/May/21…
Question Number 142344 by mnjuly1970 last updated on 30/May/21 $$ \\ $$$$\:\:\:\:\:\:\boldsymbol{\phi}:=\underset{\frac{\mathrm{1}}{{e}}} {\int}^{\:{e}} \left\{\frac{\mathrm{1}}{{ln}\left({x}\right)}+{ln}\left({ln}\left({x}\right)\right)\right\}{dx} \\ $$ Commented by Dwaipayan Shikari last updated on 30/May/21 $${log}\left({x}\right)={t}…
Question Number 142347 by mathmax by abdo last updated on 30/May/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{x}^{\mathrm{2}} \mathrm{logx}}{\mathrm{x}^{\mathrm{6}} \:+\mathrm{1}}\mathrm{dx} \\ $$ Commented by mathmax by abdo last updated…
Question Number 142346 by mathmax by abdo last updated on 30/May/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{log}\left(\mathrm{1}+\mathrm{x}^{\mathrm{3}} \right)}{\mathrm{1}+\mathrm{x}^{\mathrm{4}} }\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 76808 by aliesam last updated on 30/Dec/19 $$\int\frac{\mathrm{1}}{\:\sqrt{{x}^{\mathrm{3}} +\mathrm{1}}}{dx} \\ $$ Commented by redmiiuser last updated on 28/Mar/20 $${sir}\:{please}\:{check}\:{my}\: \\ $$$${answer} \\ $$…
Question Number 142338 by rs4089 last updated on 30/May/21 $$\int_{\mathrm{0}} ^{\infty} \frac{{sinx}}{{x}^{\mu} }{dx}\:\:=?\:\:\: \\ $$ Answered by Dwaipayan Shikari last updated on 30/May/21 $$\frac{\mathrm{1}}{{x}^{\mu} }=\frac{\mathrm{1}}{\Gamma\left(\mu\right)}\int_{\mathrm{0}}…
Question Number 76782 by mathmax by abdo last updated on 30/Dec/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{x}} \:\:\frac{{sin}\left({x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} }{dx} \\ $$ Answered by mind is power last…
Question Number 76780 by mathmax by abdo last updated on 30/Dec/19 $${find}\:{A}=\int_{−\infty} ^{+\infty} \:{x}\:{e}^{−{x}^{\mathrm{2}} } {arctan}\left({x}−\frac{\mathrm{1}}{{x}}\right){dx} \\ $$ Commented by mathmax by abdo last updated…