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} \\ $$$$\emptyset\left({x}\right)=\frac{\mathrm{1}}{\mathrm{2}}\int\:\frac{\mathrm{cos}\:{t}\:{dt}}{\:\sqrt{\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}} {t}}}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\int\:{dt}\:…
Question Number 122963 by Lordose last updated on 21/Nov/20 $$\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{x}\right)}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx} \\ $$ Answered by Dwaipayan Shikari last updated on 21/Nov/20 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}}…
Question Number 57423 by Abdo msup. last updated on 03/Apr/19 $${let}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dt}}{\left({e}^{{t}} \:+\overset{−{t}} {{e}}\right)^{{n}} } \\ $$$${calculate}\:{A}_{{n}} \:{interms}\:{of}\:{n} \\ $$ Terms of Service…
Question Number 57421 by Abdo msup. last updated on 03/Apr/19 $${calculate}\:\:\int_{−\mathrm{1}} ^{\mathrm{1}} \:\:\:\frac{\left({x}^{\mathrm{4}} \:+{x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} \:+{e}^{{x}} }{{e}^{{x}} \:+\mathrm{1}}{dx} \\ $$ Answered by einsteindrmaths@hotmail.fr last updated…
Question Number 57420 by Abdo msup. last updated on 03/Apr/19 $${let}\:{J}\left({x}\right)=\int_{\mathrm{0}} ^{{x}} \:\:\:\:\frac{{t}^{\mathrm{2}} }{\:\sqrt{{t}+\mathrm{1}}\:+\sqrt{{t}+\mathrm{4}}}{dt} \\ $$$${find}\:{a}\:{explicit}\:{form}\:{of}\:{J}\left({x}\right) \\ $$ Commented by maxmathsup by imad last updated…
Question Number 57418 by Abdo msup. last updated on 03/Apr/19 $${calculate}\:\int_{−\mathrm{1}} ^{\mathrm{4}} \:\frac{\mid{x}−\mathrm{1}\mid+\mid{x}−\mathrm{2}\mid}{\mid{x}^{\mathrm{2}} −\mathrm{9}\mid\:+{x}^{\mathrm{2}} \:+\mathrm{16}}{dx} \\ $$ Commented by kaivan.ahmadi last updated on 03/Apr/19 $$\int_{−\mathrm{1}}…