Question Number 125276 by Study last updated on 09/Dec/20 $$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\frac{{x}^{\mathrm{9}} −\mathrm{1}}{{lnx}}{dx}=??? \\ $$ Answered by Dwaipayan Shikari last updated on 09/Dec/20 $${I}\left({a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 190809 by safojontoshtemirov last updated on 12/Apr/23 Commented by Frix last updated on 12/Apr/23 $$\mathrm{Use}\:\mathrm{2}\:\mathrm{steps}: \\ $$$$\mathrm{1}.\:{t}={x}+\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{2}.\:{u}=\mathrm{2}{t}+\sqrt{\mathrm{4}{t}^{\mathrm{2}} −\mathrm{1}} \\ $$ Commented…
Question Number 59732 by maxmathsup by imad last updated on 14/May/19 $${find}\:{I}_{{n}} =\int\:\:\frac{{dx}}{{sin}^{{n}} {x}}\:\:{with}\:\:{n}\:{integr}\:{natural}. \\ $$ Answered by tanmay last updated on 14/May/19 $${I}_{{n}} =\int{cosec}^{{n}}…
Question Number 125234 by mathmax by abdo last updated on 09/Dec/20 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{\mathrm{dx}}{\mathrm{x}+\mathrm{2}+\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}}} \\ $$ Commented by john_santu last updated on 10/Dec/20 $${using}\:{Second}\:{Euler}\:{substitution}…
Question Number 125233 by mathmax by abdo last updated on 09/Dec/20 $$\mathrm{calculate}\:\mathrm{u}_{\mathrm{nm}} =\int_{\mathrm{0}} ^{\infty} \mathrm{e}^{−\mathrm{nx}} \mathrm{ln}\left(\mathrm{1}+\mathrm{e}^{\mathrm{mx}} \right)\mathrm{dx} \\ $$$$\mathrm{find}\:\sum_{\mathrm{n}\geqslant\mathrm{0}\:\mathrm{and}\:\mathrm{m}\geqslant\mathrm{0}} \:\:\mathrm{u}_{\mathrm{nm}} \\ $$ Terms of Service…
Question Number 190754 by universe last updated on 10/Apr/23 $$\:\:\:\:\:\:{I}\:\:\:=\:\:\:\:\int_{\mathrm{0}} ^{\:\pi} {e}^{{a}\mathrm{cos}\:{t}} \:\mathrm{cos}\:\left({a}\mathrm{sin}\:\:{t}\right){dt} \\ $$ Answered by namphamduc last updated on 11/Apr/23 $${I}=\int_{\mathrm{0}} ^{\pi} {e}^{{a}\mathrm{cos}\left({t}\right)}…
Question Number 59679 by Forkum Michael Choungong last updated on 13/May/19 $${Evaluate} \\ $$$$\:\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\left(\frac{{x}^{\mathrm{2}} +\mathrm{3}{x}}{{x}^{\mathrm{3}} }\right) \\ $$$$ \\ $$ Answered by Kunal12588…
Question Number 190740 by mathlove last updated on 10/Apr/23 $$\int\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{5}\right)^{\mathrm{2}} }=? \\ $$ Answered by gatocomcirrose last updated on 10/Apr/23 $$\mathrm{x}=\sqrt{\mathrm{5}}\mathrm{tg}\theta\Rightarrow\mathrm{dx}=\sqrt{\mathrm{5}}\mathrm{sec}^{\mathrm{2}} \theta\mathrm{d}\theta \\ $$$$\int\frac{\sqrt{\mathrm{5}}\mathrm{sec}^{\mathrm{2}}…
Question Number 59659 by aliesam last updated on 13/May/19 Commented by Mr X pcx last updated on 13/May/19 $${yes}\:{sir}. \\ $$ Commented by Mr X…
Question Number 125194 by bemath last updated on 09/Dec/20 $$\:\int\:\frac{\left(\mathrm{1}−\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}\right)^{\mathrm{2}} }{{x}^{\mathrm{2}} \:\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}}\:{dx}\:? \\ $$ Answered by liberty last updated on 09/Dec/20 $$\:{by}\:{second}\:{Euler}\:{substitution}\: \\…