Question Number 167400 by infinityaction last updated on 15/Mar/22 Answered by Mathspace last updated on 16/Mar/22 $${I}=\frac{\pi}{\mathrm{2}}{ln}\mathrm{2}\:+\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}{cosx}\right){dx} \\ $$$$=\frac{\pi}{\mathrm{2}}{ln}\mathrm{2}\:+{f}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)\:{with}\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\mathrm{1}+{acosx}\right){dx} \\ $$$${we}\:{take}\:\mathrm{0}<{a}\leqslant\mathrm{1}…
Question Number 101860 by Study last updated on 05/Jul/20 Commented by Study last updated on 05/Jul/20 $${what}\:{is}\:{the}\:{practice}? \\ $$ Answered by abdozaki last updated on…
Question Number 101835 by bobhans last updated on 05/Jul/20 $$\underset{\mathrm{0}} {\overset{\infty} {\int}}\frac{\mathrm{1}}{{e}^{{x}} +\mathrm{1}}\:{dx}\: \\ $$ Answered by Dwaipayan Shikari last updated on 05/Jul/20 $$\int_{\mathrm{0}} ^{\infty}…
Question Number 101833 by bobhans last updated on 05/Jul/20 $$\int\:_{−\mathrm{1}} ^{\mathrm{1}} \sqrt{\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}}\:{dx}\:?\: \\ $$ Answered by Dwaipayan Shikari last updated on 05/Jul/20 $$\int_{−\mathrm{1}} ^{\mathrm{1}} \frac{\mathrm{1}+{x}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}}…
Question Number 167366 by infinityaction last updated on 14/Mar/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 101816 by Dwaipayan Shikari last updated on 04/Jul/20 $$\int_{\mathrm{1}} ^{\:\:{e}} \left(\frac{{tan}^{−\mathrm{1}} {x}}{{x}}+\frac{{log}}{{x}^{\mathrm{2}} +\mathrm{1}}\right){dx} \\ $$ Answered by Ar Brandon last updated on 05/Jul/20…
Question Number 167355 by infinityaction last updated on 13/Mar/22 Commented by infinityaction last updated on 13/Mar/22 $${please}\:{solution}\:{of}\:{this}\:{question} \\ $$ Commented by MJS_new last updated on…
Question Number 101808 by Ar Brandon last updated on 04/Jul/20 $$\int_{\frac{\mathrm{1}}{\mathrm{3}}} ^{\mathrm{1}} \frac{\left(\mathrm{x}−\mathrm{x}^{\mathrm{3}} \right)^{\mathrm{1}/\mathrm{3}} }{\mathrm{x}^{\mathrm{4}} }\mathrm{dx} \\ $$ Answered by Dwaipayan Shikari last updated on…
Question Number 167328 by cortano1 last updated on 13/Mar/22 $$\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\pi/\mathrm{2}} \:\frac{\mathrm{cos}\:{x}+\mathrm{cos}\:^{\mathrm{5}} {x}\:\mathrm{sin}\:{x}}{\:\sqrt{\mathrm{1}+\mathrm{cos}\:^{\mathrm{2}} {x}}}\:{dx}\:=? \\ $$ Answered by MJS_new last updated on 13/Mar/22 $$\int\frac{\mathrm{cos}\:{x}\:+\mathrm{cos}^{\mathrm{5}} \:{x}\:\mathrm{sin}\:{x}}{\:\sqrt{\mathrm{1}+\mathrm{cos}^{\mathrm{2}}…
Question Number 101793 by Dwaipayan Shikari last updated on 04/Jul/20 $$\int_{\mathrm{1}} ^{\mathrm{2}} \frac{{logu}}{\left(\sqrt{{u}−\mathrm{1}}\right)\left(\sqrt{{u}−\mathrm{1}}+\mathrm{1}\right)}{du} \\ $$ Answered by mathmax by abdo last updated on 05/Jul/20 $$\mathrm{I}\:=\int_{\mathrm{1}}…