Question Number 116112 by Lordose last updated on 01/Oct/20 $$\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}}\: \\ $$$$\int_{\:\mathrm{0}} ^{\:\infty} \frac{\boldsymbol{\mathrm{lnx}}}{\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\boldsymbol{\mathrm{dx}}\:=\:\mathrm{0} \\ $$$$ \\ $$ Answered by MJS_new last updated on…
Question Number 181643 by Frix last updated on 28/Nov/22 $$\Omega=\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\mathrm{tan}^{−\mathrm{1}} \:\mathrm{cos}\:{x}\:{dx} \\ $$$$\left(\mathrm{I}'\mathrm{d}\:\mathrm{need}\:\mathrm{the}\:\mathrm{exact}\:\mathrm{value}\:\mathrm{if}\:\mathrm{possible}.\:\mathrm{I}'\mathrm{ve}\right. \\ $$$$\left.\mathrm{got}\:\mathrm{no}\:\mathrm{idea}\:\mathrm{if}\:\mathrm{and}\:\mathrm{how}\:\mathrm{this}\:\mathrm{can}\:\mathrm{be}\:\mathrm{solved}.\right) \\ $$ Commented by MJS_new last updated on…
Question Number 116096 by mathmax by abdo last updated on 30/Sep/20 $$\mathrm{find}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{lnx}}{\mathrm{x}^{\mathrm{2}} −\mathrm{i}}\mathrm{dx}\:\:\:\:\:\left(\mathrm{i}=\sqrt{−\mathrm{1}}\right) \\ $$ Answered by mindispower last updated on 01/Oct/20 $${let}\:{f}\left({z}\right)=\frac{{ln}\left({z}\right)}{{z}^{\mathrm{2}}…
Question Number 116098 by mathmax by abdo last updated on 30/Sep/20 $$\left.\mathrm{1}\right)\mathrm{calculate}\:\mathrm{f}\left(\mathrm{x}\right)=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\frac{\mathrm{d}\theta}{\mathrm{x}^{\mathrm{2}} −\mathrm{2x}\:\mathrm{cos}\theta\:+\mathrm{1}}\:\:\:\:\mathrm{0}<\theta<\frac{\pi}{\mathrm{2}} \\ $$$$\left.\mathrm{2}\right)\mathrm{explicite}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{\mathrm{cos}\theta}{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{2xcos}\theta\:+\mathrm{1}\right)^{\mathrm{2}} }\mathrm{d}\theta \\ $$ Terms of…
Question Number 116097 by mathmax by abdo last updated on 30/Sep/20 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{lnx}}{\mathrm{x}^{\mathrm{4}} \:+\mathrm{1}}\mathrm{dx}\: \\ $$ Answered by mnjuly1970 last updated on 01/Oct/20 $$\:\:{solution}:\:\:\:\Omega=\int_{\mathrm{0}}…
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Question Number 116016 by bemath last updated on 30/Sep/20 $$\underset{−\mathrm{1}} {\overset{\mathrm{1}} {\int}}\:\frac{{dx}}{\:\sqrt{\mathrm{6}+{x}−{x}^{\mathrm{2}} }}\:? \\ $$ Answered by bobhans last updated on 30/Sep/20 $${I}=\underset{−\mathrm{1}} {\overset{\mathrm{1}} {\int}}\:\frac{{dx}}{\:\sqrt{\mathrm{6}−\left({x}^{\mathrm{2}}…
Question Number 116014 by mnjuly1970 last updated on 30/Sep/20 $$\:\:\:\:\:\:\:…{nice}\:\:{calculus}\:…\:\:\: \\ $$$$\:{prove}\:: \\ $$$$\:\:\:{i}:\int_{\mathrm{0}} ^{\:\infty} \frac{{ln}\left({x}\right)}{\left(\mathrm{1}+{x}^{\sqrt{\mathrm{2}}} \right)^{\sqrt{\mathrm{2}}} }\:=\mathrm{0}\:\:\:\:\:\:\checkmark \\ $$$$\:\:\:{ii}:\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{1}+\sqrt{\mathrm{2}}} \right)^{\mathrm{1}+\sqrt{\mathrm{2}}} }\:=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:\:\checkmark\:\: \\…
Question Number 116000 by frc2crc last updated on 30/Sep/20 $${U}\left({n}\right)=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{1}−\mathrm{tanh}\:{x}}{\:\sqrt[{{n}}]{\mathrm{tanh}\:{x}}}{dx} \\ $$$${another}\:{way}? \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 115974 by jm2bok last updated on 29/Sep/20 $$\int\frac{{e}^{\mathrm{3}{x}} −{e}^{{x}} }{{x}\left({e}^{\mathrm{3}{x}} +\mathrm{1}\right)\left({e}^{{x}} +\mathrm{1}\right)}{dx}\:=\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com