Question Number 179175 by Acem last updated on 26/Oct/22 $$\:{Find}\:\int{x}^{\mathrm{5}} \:\sqrt{{x}^{\mathrm{3}} +\mathrm{1}}\:{dx} \\ $$$$\: \\ $$$$\:{Answer}:\:{I}=\:\frac{\mathrm{2}}{\mathrm{45}}\:\left(\mathrm{3}{x}^{\mathrm{3}} −\mathrm{2}\right)\:\sqrt{\left({x}^{\mathrm{3}} +\mathrm{1}\right)^{\mathrm{3}} }\:+\:{c} \\ $$$$ \\ $$ Commented by…
Question Number 113634 by eric last updated on 14/Sep/20 $${Bonjour}\:{besoin}\:{d}'{aide} \\ $$$${Calculer}\:\int{ln}\left({cosx}\right){dx} \\ $$ Answered by Olaf last updated on 14/Sep/20 $$\mathrm{cos}{x}\:=\:\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{k}} {x}^{\mathrm{2}{k}}…
Question Number 113630 by mathmax by abdo last updated on 14/Sep/20 $$\mathrm{explicit}\:\mathrm{g}\left(\mathrm{a}\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\mathrm{ln}\left(\mathrm{1}+\mathrm{acos}^{\mathrm{2}} \theta\right)\mathrm{d}\theta \\ $$ Answered by Dwaipayan Shikari last updated on 15/Sep/20…
Question Number 113629 by mathmax by abdo last updated on 14/Sep/20 $$\mathrm{find}\:\mathrm{f}\left(\mathrm{a}\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{8}}} \:\mathrm{ln}\left(\mathrm{1}+\mathrm{a}\:\mathrm{sin}\theta\right)\mathrm{d}\theta\:\:\:\mathrm{with}\:\mathrm{o}<\mathrm{a}<\mathrm{1} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 113628 by mathmax by abdo last updated on 14/Sep/20 $$\mathrm{find}\:\int\:\:\frac{\mathrm{dx}}{\left(\mathrm{x}+\mathrm{1}\right)\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}+\left(\mathrm{x}−\mathrm{1}\right)\sqrt{\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}}} \\ $$ Answered by MJS_new last updated on 16/Sep/20 $$\int\frac{{dx}}{\left({x}+\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}+\left({x}−\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}}…
Question Number 113627 by mathmax by abdo last updated on 14/Sep/20 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{4}} +\mathrm{ix}^{\mathrm{2}} \:+\mathrm{2}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 48078 by cesar.marval.larez@gmail.com last updated on 19/Nov/18 Answered by tanmay.chaudhury50@gmail.com last updated on 19/Nov/18 $$\left.\mathrm{21}\right)\int{e}^{\mathrm{2}−{x}} {dx} \\ $$$${t}=\mathrm{2}−{x}\:\:\:{dt}=−{dx} \\ $$$$\int{e}^{{t}} ×−{dt} \\ $$$$=\left(−\mathrm{1}\right){e}^{{t}}…
Question Number 48067 by maxmathsup by imad last updated on 18/Nov/18 $${let}\:{y}>\mathrm{0}\:{give}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{x}^{{y}} }{{e}^{{x}} −\mathrm{1}}{dx}\:{at}\:{form}\:{of}\:{series}. \\ $$ Commented by maxmathsup by imad last updated…
Question Number 113600 by eric last updated on 14/Sep/20 $${Prouver}\:{que} \\ $$$$\beta\left({a},{b}\right)=\frac{\Gamma\left({a}\right)\Gamma\left({b}\right)}{\Gamma\left({a}+{b}\right)}=\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{{a}−\mathrm{1}} \left(\mathrm{1}−{x}\right)^{{b}−\mathrm{1}} {dx} \\ $$ Answered by Dwaipayan Shikari last updated on…
Question Number 48064 by maxmathsup by imad last updated on 18/Nov/18 $${calculate}\:{A}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}+{x}^{\mathrm{2}} \right)\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }{dx}\:\:−\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right)\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$ Commented by maxmathsup…