Question Number 91910 by Ar Brandon last updated on 03/May/20 $$\int\frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{sin}^{\mathrm{2}} \mathrm{x}\right)}{\mathrm{sin}^{\mathrm{2}} \mathrm{x}}\mathrm{dx} \\ $$ Commented by mathmax by abdo last updated on 03/May/20 $${let}\:{f}\left({a}\right)\:=\int\frac{{ln}\left(\mathrm{1}+{asin}^{\mathrm{2}}…
Question Number 157442 by bobhans last updated on 23/Oct/21 $$\:\:\int\:\frac{\mathrm{dx}}{\mathrm{x}−\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{2}}}\: \\ $$ Answered by MJS_new last updated on 23/Oct/21 $$\int\frac{{dx}}{{x}−\sqrt{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{2}}}= \\ $$$$\:\:\:\:\:\left[{t}={x}+\mathrm{1}+\sqrt{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{2}}\:\rightarrow\:{dx}=\frac{\sqrt{{x}^{\mathrm{2}}…
Question Number 91904 by Ar Brandon last updated on 03/May/20 $$\int_{\mathrm{1}} ^{\mathrm{e}^{\pi} } \frac{\mathrm{cos}\left(\mathrm{lnx}\right)}{\mathrm{x}}\mathrm{dx} \\ $$ Commented by Prithwish Sen 1 last updated on 03/May/20…
Question Number 26362 by abdo imad last updated on 24/Dec/17 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\propto} {e}^{−{x}} {lnx}\:{dx}\:\:\:{for}\:{that}\:{use} \\ $$$${A}_{{n}} \:\:=\:\:\:\int_{\mathrm{0}} ^{{n}} \:\left(\mathrm{1}−\:\frac{{t}}{{n}}\right)^{{n}−\mathrm{1}} {ln}\left({t}\right)\:{dt}\:\:. \\ $$ Terms of Service…
Question Number 26359 by abdo imad last updated on 24/Dec/17 $${find}\:\:\:{lim}_{{n}−>\propto} \:\:\int_{\mathrm{0}} ^{{n}} \:\left(\mathrm{1}−\frac{{t}}{{n}}\right)^{{n}−\mathrm{1}} {dt}\:\:\:. \\ $$ Commented by abdo imad last updated on 25/Dec/17…
Question Number 26360 by abdo imad last updated on 24/Dec/17 $$\:\:{find}\:{the}\:{value}\:{of}\:\:\:\:\int_{\mathrm{0}} ^{\:\propto\:} \:\frac{{cos}\left(\alpha{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}\:\:. \\ $$ Commented by abdo imad last updated on 25/Dec/17 $${let}\:{put}\:{I}=\:\:\int_{\mathrm{0}}…
Question Number 26357 by abdo imad last updated on 24/Dec/17 $${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{ln}\left({cos}\theta\right){d}\theta\:\:{and}\: \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{ln}\left({sin}\theta\right){d}\theta\:\:\:. \\ $$ Commented by prakash jain last updated…
Question Number 91892 by john santu last updated on 03/May/20 $$\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\frac{{dx}}{{a}^{\mathrm{2}} \mathrm{cos}\:^{\mathrm{2}} {x}+{b}^{\mathrm{2}} \:\mathrm{sin}\:^{\mathrm{2}} {x}}\:? \\ $$ Commented by john santu last updated…
Question Number 26358 by abdo imad last updated on 24/Dec/17 $${find}\:{the}\:{value}\:{of}\:\:\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:{tan}^{{n}} {x}\:{dx}\:\:\:\:{with}\: \\ $$$${n}\:\:{element}\:{from}\:\mathbb{N}. \\ $$ Answered by prakash jain last updated on…
Question Number 157412 by cortano last updated on 23/Oct/21 $$\:\int_{\:\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\frac{{x}}{\mathrm{sin}\:^{\mathrm{8}} {x}+\mathrm{cos}\:^{\mathrm{8}} {x}}\:{dx}\:? \\ $$ Answered by phanphuoc last updated on 23/Oct/21 $$\int_{\mathrm{0}} ^{\pi/\mathrm{2}}…