Question Number 118111 by bemath last updated on 15/Oct/20 $$\underset{\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\:\frac{\mathrm{x}^{\mathrm{2}} }{\left(\mathrm{x}\:\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}\right)^{\mathrm{2}} }\:\mathrm{dx}\:=? \\ $$ Answered by Lordose last updated on 15/Oct/20 $$ \\…
Question Number 118094 by bemath last updated on 15/Oct/20 $$\int\:\frac{\mathrm{dx}}{\mathrm{sec}\:\mathrm{x}+\mathrm{2}}\:=? \\ $$ Answered by Dwaipayan Shikari last updated on 15/Oct/20 $$\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{2}{cosxdx}}{\mathrm{2}{cosx}+\mathrm{1}}=\frac{\mathrm{1}}{\mathrm{2}}\int\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}{cosx}+\mathrm{1}}{dx} \\ $$$$=\frac{{x}}{\mathrm{2}}−\int\frac{\mathrm{1}}{\frac{\mathrm{2}−\mathrm{2}{t}^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{2}} }+\mathrm{1}}.\frac{\mathrm{1}}{\mathrm{1}+{t}^{\mathrm{2}}…
Question Number 52550 by Tawa1 last updated on 09/Jan/19 $$\:\:\int_{\mathrm{0}} ^{\:\infty} \:\:\:\frac{\mathrm{x}}{\mathrm{e}^{\mathrm{x}} \:−\:\mathrm{1}}\:\:\mathrm{dx}\: \\ $$ Commented by maxmathsup by imad last updated on 11/Jan/19 $${let}\:{I}\:=\int_{\mathrm{0}}…
Question Number 118084 by bemath last updated on 15/Oct/20 $$\mathrm{suppose}\:\mathrm{f}:\:\left[\mathrm{1},\mathrm{3}\:\right]\rightarrow\:\left[−\mathrm{1},\mathrm{1}\:\right]\:\mathrm{such} \\ $$$$\mathrm{that}\:\underset{\mathrm{1}} {\overset{\mathrm{3}} {\int}}\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:=\:\mathrm{0}\:.\:\mathrm{What}\:\mathrm{the}\:\mathrm{maximum} \\ $$$$\mathrm{value}\:\mathrm{of}\:\underset{\mathrm{1}} {\overset{\mathrm{3}} {\int}}\:\mathrm{x}^{−\mathrm{1}} .\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:? \\ $$ Commented by john santu…
Question Number 118081 by bemath last updated on 15/Oct/20 $$\:\int\:\mathrm{arc}\:\mathrm{cos}\:\left(\frac{\mathrm{cos}\:\mathrm{x}}{\mathrm{1}+\mathrm{2cos}\:\mathrm{x}}\right)\:\mathrm{dx}\:=? \\ $$ Commented by MJS_new last updated on 15/Oct/20 $$\mathrm{seems}\:\mathrm{impossible}\:\mathrm{to}\:\mathrm{solve} \\ $$ Commented by MJS_new…
Question Number 118073 by bemath last updated on 15/Oct/20 $$\mathrm{Evaluate}\:\underset{\mathrm{0}} {\overset{{a}} {\int}}\:{b}\sqrt{\mathrm{1}−\frac{\mathrm{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }}\:{dx}\: \\ $$ Answered by john santu last updated on 15/Oct/20 $${I}=\underset{\mathrm{0}}…
Question Number 118030 by mathmax by abdo last updated on 14/Oct/20 $$\mathrm{find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{2}}{\mathrm{x}^{\mathrm{4}} +\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}}\mathrm{dx} \\ $$ Commented by Ar Brandon last updated…
Question Number 183559 by cortano1 last updated on 27/Dec/22 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{\mathrm{1}} {\overset{\infty} {\int}}\:\frac{{dx}}{{x}^{\mathrm{2}} +\sqrt{{x}}}\:=\:?\: \\ $$ Answered by greougoury555 last updated on 27/Dec/22 $$\:\:\:{G}\:=\:\int_{\mathrm{1}} ^{\:\infty} \:\frac{{dx}}{{x}^{\mathrm{2}}…
Question Number 52484 by Tawa1 last updated on 08/Jan/19 $$\int\:\:\frac{\mathrm{cos}\:\mathrm{x}\:−\:\mathrm{x}\:\mathrm{sin}\:\mathrm{x}}{\mathrm{x}\:\mathrm{cos}\:\mathrm{x}}\:\:\mathrm{dx} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 08/Jan/19 $$\int\frac{{dx}}{{x}}−\int{tanxdx} \\ $$$${lnx}−{lnsecx}+{c} \\ $$ Commented…
Question Number 52482 by maxmathsup by imad last updated on 08/Jan/19 $${find}\:{the}\:{value}\:{or}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{arctan}\left({x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}^{\mathrm{4}} }{dx}\:. \\ $$ Commented by Abdo msup. last updated on…