Question Number 57490 by Abdo msup. last updated on 05/Apr/19 $$\left.\mathrm{1}\right){findF}\left({a}\right)=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{cos}\left({ln}\left(\mathrm{2}+{x}^{\mathrm{2}} \right)\right)}{{a}^{\mathrm{2}} \:+{x}^{\mathrm{2}} }{dx}\:\:{witha}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cos}\left({ln}\left(\mathrm{2}+{x}^{\mathrm{2}} \right)\right)}{\mathrm{4}+{x}^{\mathrm{2}} }{dx}. \\ $$ Commented…
Question Number 57487 by Abdo msup. last updated on 05/Apr/19 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{1}} \:\:\:\int_{{x}} ^{{x}^{\mathrm{2}} } \:\:\:\:\frac{{arctan}\left({t}\right)}{{sint}}{dt}\:. \\ $$ Commented by kaivan.ahmadi last updated on 05/Apr/19 $${zero}…
Question Number 123023 by mnjuly1970 last updated on 21/Nov/20 $$\:\:\:\:\:\:\:\:\:\:…\:{advanced}\:\:{calculus}… \\ $$$${calculate}::: \\ $$$$\:\:\:\:\:\mathrm{I}:\overset{???} {=}\:\int_{\mathrm{0}} ^{\:\pi} \frac{{x}}{\mathrm{1}−{sin}\left({x}\right){cos}\left({x}\right)}{dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:………………………….. \\ $$ Answered by mnjuly1970 last…
Question Number 123020 by mnjuly1970 last updated on 21/Nov/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{advanced}\:\:{calculus}.. \\ $$$$ \\ $$$$\:\:\:{calculate}\:::\:\:\:\emptyset=\int_{\mathrm{0}} ^{\:\pi} \frac{\pi}{\mathrm{1}−{sin}\left({x}\right){cos}\left({x}\right)}{dx}=??? \\ $$$$\:\:\:\:\:\:\:\:……………….. \\ $$ Answered by Dwaipayan Shikari last…
Question Number 188552 by normans last updated on 03/Mar/23 Commented by normans last updated on 03/Mar/23 $$\:{use}\:{a}\:{quick}\:{trick}\:{to}\:{solve}\:{the}\:{problem}. \\ $$$$\:{thank}\:{you}..\: \\ $$ Terms of Service Privacy…
Question Number 122980 by liberty last updated on 21/Nov/20 $$\:\int_{\mathrm{0}} ^{\ell{n}\:\mathrm{10}} \:\frac{{e}^{{x}} \:\sqrt{{e}^{{x}} −\mathrm{1}}}{{e}^{{x}} +\mathrm{8}}\:{dx}\:? \\ $$ Answered by bemath last updated on 21/Nov/20 Answered…
Question Number 122979 by bemath last updated on 21/Nov/20 $$\:\:\int_{\mathrm{0}} ^{\pi} \frac{{x}\:\mathrm{sin}\:{x}}{\:\sqrt{\mathrm{3}+\mathrm{sin}\:^{\mathrm{2}} {x}}}\:{dx}\:? \\ $$ Answered by liberty last updated on 21/Nov/20 $$\psi\left({x}\right)=\int_{\mathrm{0}} ^{\pi} \frac{{x}\mathrm{sin}\:{x}}{\:\sqrt{\mathrm{4}−\mathrm{cos}\:^{\mathrm{2}}…
Question Number 122976 by bemath last updated on 21/Nov/20 $$\:\int_{\mathrm{1}} ^{\:\infty} \:\frac{\mathrm{tan}^{−\mathrm{1}} \left({x}\right)}{{x}^{\mathrm{2}} }\:{dx}\:? \\ $$ Answered by mnjuly1970 last updated on 21/Nov/20 $${solution}:: \\…
Question Number 188511 by universe last updated on 02/Mar/23 $$\:\:\:{evaluate} \\ $$$$\int_{\mathrm{0}} ^{\pi} \frac{{dx}}{{a}+{b}\mathrm{cos}{x}\:}\:\:\:\:\:\:,\:\:\:{a}\:>\:\mathrm{0} \\ $$$$\:\:\:{and}\:{deduce}\:{that} \\ $$$$\:\:\:\int_{\mathrm{0}} ^{\pi} \frac{{dx}}{\left({a}+{b}\mathrm{cos}\:{x}\right)^{\mathrm{2}} }\:\:=\:\:\:\frac{\pi{a}}{\left({a}^{\mathrm{2}} −{b}^{\mathrm{2}} \right)^{\mathrm{3}/\mathrm{2}} }\:\:;\:\:{a}^{\mathrm{2}} >{b}^{\mathrm{2}}…
Question Number 122967 by bemath last updated on 21/Nov/20 $$\:\:\int\:\frac{{x}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{4}} }}\:{dx}\: \\ $$ Answered by bobhans last updated on 21/Nov/20 $${let}\:{x}^{\mathrm{2}} \:=\:\mathrm{sin}\:{t}\:\Rightarrow\:\mathrm{2}{x}\:{dx}\:=\:\mathrm{cos}\:{t}\:{dt} \\ $$$$\emptyset\left({x}\right)=\frac{\mathrm{1}}{\mathrm{2}}\int\:\frac{\mathrm{cos}\:{t}\:{dt}}{\:\sqrt{\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}} {t}}}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\int\:{dt}\:…