Category: Integration

Question Number 137991 by EnterUsername last updated on 08/Apr/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}^{\mathrm{3}} \left({sinx}\right){dx} \\ $$ Answered by Ar Brandon last updated on 08/Apr/21 $$\mathrm{f}\left(\alpha\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…

Question Number 137973 by mnjuly1970 last updated on 08/Apr/21 $$\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:…….{Advanced}\:…\:…\:…\:…\:{Calculus}……. \\ $$$$\:\:\:\:{prove}\:{that}::: \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left(\mathrm{1}−{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}=\frac{\pi}{\mathrm{8}}{ln}\left(\mathrm{2}\right)−{G}\:…\checkmark \\ $$$$\:\:\:\:{where}\:\:{G}\:{is}\:{catalan}\:{number}… \\ $$$$\:\:\: \\ $$…

Question Number 137971 by EnterUsername last updated on 08/Apr/21 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{x}} \left(\mathrm{x}−\mathrm{t}\right)\mathrm{t}^{\mathrm{2}} \sqrt[{\mathrm{3}}]{\mathrm{y}\left(\mathrm{t}\right)}\mathrm{dt}+\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\mathrm{x}} \left(\mathrm{5x}−\mathrm{6t}\right)\mathrm{y}\left(\mathrm{t}\right)\mathrm{dt}+\mathrm{2x}=\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact:…

Question Number 137940 by benjo_mathlover last updated on 08/Apr/21 $$\int_{\mathrm{1}} ^{\:{e}} \sqrt{\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }+\frac{\mathrm{1}}{\left({x}+\mathrm{1}\right)^{\mathrm{2}\:} }}\:{dx}\:=? \\ $$ Answered by john_santu last updated on 08/Apr/21 $$\mathcal{J}\:=\:\int_{\mathrm{1}} ^{\:{e}}…

Question Number 6865 by Tawakalitu. last updated on 31/Jul/16 $$\int\frac{{sin}\left({x}\right)\:+\:{cos}\left({x}\right)}{{e}^{−{x}} \:+\:{sin}\left({x}\right)}\:{dx} \\ $$ Commented by Yozzii last updated on 31/Jul/16 $${sinhix}={isinx} \\ $$$${sinx}=\frac{{sinhix}}{{i}}=\frac{{e}^{{ix}} −{e}^{−{ix}} }{\mathrm{2}{i}}…