Question Number 109212 by mathmax by abdo last updated on 22/Aug/20 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\pi} \:\frac{\mathrm{sin}\left(\mathrm{nx}\right)}{\mathrm{cosx}}\mathrm{dx}\:\:\mathrm{with}\:\mathrm{n}\:\mathrm{integr} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 43675 by maxmathsup by imad last updated on 13/Sep/18 $${calculate}\:\:\:\:\:\int_{\mathrm{1}} ^{\mathrm{2}} \:\:\:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{4}} }\:. \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 43676 by maxmathsup by imad last updated on 13/Sep/18 $$\left.\mathrm{1}\right){calculate}\:\:{I}\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{{x}^{\mathrm{2}} −{i}}\:\:{and}\:\:{J}\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{{x}^{\mathrm{2}} \:+{i}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{{x}^{\mathrm{4}} \:+\mathrm{1}} \\ $$…
Question Number 43657 by Tinkutara last updated on 13/Sep/18 Commented by maxmathsup by imad last updated on 24/Sep/18 $${let}\:{A}\:=\:\int\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:+\mathrm{2}{x}\:+\mathrm{10}\right)^{\mathrm{2}} }\:{we}\:{have}\:{A}\:=\int\:\:\:\frac{{dx}}{\left\{\left({x}+\mathrm{1}\right)^{\mathrm{2}} \:+\mathrm{9}\right\}^{\mathrm{2}} } \\ $$$${changement}\:{x}+\mathrm{1}\:=\mathrm{3}{tan}\theta\:{give}\:…
Question Number 174727 by princeDera last updated on 09/Aug/22 $$\int_{\mathrm{0}} ^{\infty} \frac{{e}^{−{x}^{\mathrm{2}} } }{\left({x}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx} \\ $$ Answered by aleks041103 last updated on…
Question Number 174696 by mnjuly1970 last updated on 08/Aug/22 $$ \\ $$$$\:\:\:\:\:\boldsymbol{{prove}}\:\:\boldsymbol{{that}}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{\Omega}\:=\:\int_{\mathrm{0}} ^{\:\infty} \left(\:\frac{\:\boldsymbol{{x}}}{\:\boldsymbol{{sinh}}\:\left(\boldsymbol{{x}}\right)}\:\right)^{\:\mathrm{3}} \boldsymbol{{dx}}\:=\frac{\boldsymbol{\pi}^{\:\mathrm{2}} }{\mathrm{16}}\:\left(\mathrm{12}−\:\boldsymbol{\pi}^{\:\mathrm{2}} \right)\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{{written}}\:\:\boldsymbol{{and}}\:\boldsymbol{{prepared}}\:\boldsymbol{{by}}\::\:\:\boldsymbol{{m}}.\boldsymbol{{n}}\:\:\:\:\:\:\:\: \\ $$$$…
Question Number 43623 by math khazana by abdo last updated on 12/Sep/18 $${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{{x}} \:\frac{{dt}}{\mathrm{1}+{t}^{\mathrm{4}} } \\ $$$$\left.\mathrm{1}\right)\:{find}\:\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dt}}{\mathrm{1}+{t}^{\mathrm{4}} } \\ $$…
Question Number 174685 by mnjuly1970 last updated on 08/Aug/22 $$ \\ $$$$\:\:\:\:\:{prove}\:{that}\:: \\ $$$$\: \\ $$$$\:\:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:\:{x}^{\:\mathrm{2}} }{{cosh}\left({x}\:\right)}\:{dx}\:=\:\frac{\pi^{\:\mathrm{3}} }{\:\mathrm{8}} \\ $$$$ \\ $$ Answered…
Question Number 109136 by EmericGent last updated on 21/Aug/20 $$\int_{\mathrm{0}} ^{\mathrm{1}/\mathrm{2}} \frac{{ln}\left(\mathrm{1}-{t}\right){ln}\left({t}\right)}{{t}}\:{dt} \\ $$$${I}'{m}\:{about}\:{to}\:{give}\:{up} \\ $$ Answered by Sarah85 last updated on 21/Aug/20 $$\int\frac{\mathrm{ln}\:\left(\mathrm{1}−{t}\right)\:\mathrm{ln}\:{t}}{{t}}{dt} \\…
Question Number 109129 by bemath last updated on 21/Aug/20 $$\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\frac{\mathrm{ln}\:\left(\mathrm{cos}\:{x}\right)\mathrm{ln}\:\left(\mathrm{sin}\:{x}\right)}{\mathrm{tan}\:{x}}\:{dx} \\ $$ Answered by EmericGent last updated on 21/Aug/20 $$=\:{I}\:=\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \frac{{ln}\left(\mathrm{1}-{sin}^{\mathrm{2}} {x}\right){ln}\left({sin}\:{x}\right)}{{sin}\:{x}}\:{cos}\:{x}\:{dx}…