Question Number 5058 by Yozzii last updated on 06/Apr/16 $$\int\int\frac{{a}}{\left(\mathrm{1}−{lnx}\right)\left({lny}−\mathrm{1}\right)}{dxdy}=? \\ $$ Commented by Yozzii last updated on 06/Apr/16 $$\int\int\int\int…\int\int\int\frac{{a}}{\underset{{i}=\mathrm{1}} {\overset{{n}} {\prod}}\left(\mathrm{1}−{lnx}_{{i}} \right)}{dx}_{\mathrm{1}} {dx}_{\mathrm{2}} …{dx}_{{n}}…
Question Number 70571 by ahmadshahhimat775@gmail.com last updated on 05/Oct/19 Commented by mathmax by abdo last updated on 05/Oct/19 $$\left.\exists\:{c}\:\in\right]\mathrm{3},\mathrm{3}+{h}\left[\:/\int_{\mathrm{3}} ^{{h}+\mathrm{3}} \:\frac{\mathrm{5}{dx}}{{x}^{\mathrm{3}} \:+\mathrm{7}}\:=\frac{\mathrm{5}}{{c}^{\mathrm{3}} \:+\mathrm{7}}\:\int_{\mathrm{3}} ^{{h}+\mathrm{3}} {dx}=\frac{\mathrm{5}{h}}{{c}^{\mathrm{3}}…
Question Number 5032 by gourav~ last updated on 04/Apr/16 $$\int\frac{{ax}+{b}}{\left({cx}+{d}\right)^{\mathrm{2}} }{dx}\:=? \\ $$$$ \\ $$ Answered by Yozzii last updated on 04/Apr/16 $${Let}\:{u}={cx}+{d}\Rightarrow{du}={cdx}\Rightarrow{c}^{−\mathrm{1}} {du}={dx}. \\…
Question Number 5026 by gourav~ last updated on 04/Apr/16 $$\int\frac{\mathrm{16}}{{x}^{\mathrm{2}} \sqrt{\mathrm{4}−\mathrm{9}{x}^{\mathrm{2}} }}{dx}\:=? \\ $$$$ \\ $$ Answered by Yozzii last updated on 04/Apr/16 $${Let}\:{x}=\frac{\mathrm{2}}{\mathrm{3}}{cosy}\Rightarrow{dx}=−\frac{\mathrm{2}}{\mathrm{3}}{sinydy} \\…
Question Number 136076 by physicstutes last updated on 18/Mar/21 $$\mathrm{find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{between}\:\mathrm{the}\:\mathrm{curve}\:{y}\:=\:\mathrm{3}\:+\:\mathrm{2}{x}\:−{x}^{\mathrm{2}} ,\:\mathrm{the}\:{x}−\mathrm{axis} \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{line}\:{y}\:=\:\mathrm{3}. \\ $$$$\:\mathrm{find}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{the}\:\mathrm{solid}\:\mathrm{generated}\:\mathrm{when}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{is} \\ $$$$\mathrm{rotated}\:\mathrm{completely}\:\mathrm{about}\:\mathrm{the}\:\mathrm{line}\:{y}\:=\:\mathrm{3} \\ $$ Answered by mr W last updated…
Question Number 136067 by bramlexs22 last updated on 18/Mar/21 $$\Lambda\:=\:\int\:{x}^{\mathrm{3}} \:\left({x}^{\mathrm{3}} +\mathrm{1}\right)^{\mathrm{10}} \:{dx}\: \\ $$ Answered by Olaf last updated on 18/Mar/21 $$\Lambda\:=\:\int{x}^{\mathrm{3}} \left({x}^{\mathrm{3}} +\mathrm{1}\right)^{\mathrm{10}}…
Question Number 136060 by mnjuly1970 last updated on 18/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…{advanced}\:\:\:{calculus}…. \\ $$$$\:\:\:\:{evaluate}:: \\ $$$$\:\:\:\:\boldsymbol{\phi}=\mathrm{Im}\left(\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {li}_{\mathrm{2}} \left({sin}\left({x}\right)\right)+{li}_{\mathrm{2}} \left({csc}\left({x}\right)\right){dx}\right) \\ $$$$ \\ $$ Answered by mindispower…
Question Number 136036 by mathmax by abdo last updated on 18/Mar/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{logx}}{\mathrm{x}^{\mathrm{4}} \:+\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}}\mathrm{dx} \\ $$ Commented by Ajetunmobi last updated on 18/Mar/21…
Question Number 136034 by mathmax by abdo last updated on 18/Mar/21 $$\mathrm{calculate}\:\int_{−\infty} ^{+\infty} \:\frac{\mathrm{cos}\left(\mathrm{2x}\right)\mathrm{dx}}{\mathrm{x}^{\mathrm{4}} \:+\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}} \\ $$$$ \\ $$ Answered by mathmax by abdo…
Question Number 4957 by ankit chakravarti last updated on 26/Mar/16 $$\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{4}{x}^{\mathrm{3}} \left\{\frac{{d}^{\mathrm{2}} }{{dx}^{\mathrm{2}} }\left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{\mathrm{5}} \right\}{dx}=? \\ $$ Commented by ankit chakravarti last…