Question Number 64745 by mathmax by abdo last updated on 21/Jul/19 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{sin}\left({lnx}\right)}{{lnx}}{dx} \\ $$ Commented by mathmax by abdo last updated on 21/Jul/19…
Question Number 64733 by mmkkmm000m last updated on 20/Jul/19 $$\int\left({sec}\theta{tan}\theta\right){d}\theta/{sec}\theta\overset{−} {+}{tan}\theta \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 64735 by mmkkmm000m last updated on 20/Jul/19 $$\int{tan}\theta/\mathrm{1}\overset{−} {+}{sin}\theta\:{d}\theta \\ $$ Commented by mr W last updated on 21/Jul/19 $${dear}\:{sir}: \\ $$$${in}\:{Q}\mathrm{64238}\:{i}\:{asked}\:{if}\:{you}\:{could}\:{use} \\…
Question Number 130254 by Eric002 last updated on 23/Jan/21 $${prove} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{{ln}^{\mathrm{2}} \left({x}\right){ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}=\frac{\mathrm{7}\pi}{\mathrm{4}}\zeta\left(\mathrm{3}\right)+\frac{\pi^{\mathrm{3}} {ln}\left(\mathrm{2}\right)}{\mathrm{4}} \\ $$$${where}\:\zeta\left(\mathrm{3}\right)\:{is}\:{a}\:{pery}^{\:,} {s}\:{constant} \\ $$ Answered by…
Question Number 64687 by aliesam last updated on 20/Jul/19 Commented by mathmax by abdo last updated on 21/Jul/19 $${let}\:{A}\:=\int\:\:\:\frac{{e}^{\frac{−{cos}\left(\mathrm{2}{x}\right)}{\mathrm{2}}} }{{sin}^{\mathrm{2}} {x}}\:{dx}\:\Rightarrow\:{A}\:=\int\:\:\:\frac{{e}^{−\frac{{cos}\left(\mathrm{2}{x}\right)}{\mathrm{2}}} }{\frac{\mathrm{1}−{cos}\left(\mathrm{2}{x}\right)}{\mathrm{2}}}\:{dx} \\ $$$$=\:\mathrm{2}\:\int\:\:\:\frac{{e}^{−\frac{{cos}\left(\mathrm{2}{x}\right)}{\mathrm{2}}} }{\mathrm{1}−{cos}\left(\mathrm{2}{x}\right)}{dx}\:\:\:{changement}\:{cos}\left(\mathrm{2}{x}\right)\:={t}\:{give}\:\mathrm{2}{x}={argch}\left({t}\right)…
Question Number 64677 by mathmax by abdo last updated on 20/Jul/19 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} {lnt}\:{ln}\left(\mathrm{1}−{xt}\right){dt}\:\:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{1}\right){determine}\:{a}\:{explicit}\:{form}\:{for}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{also}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{tlnt}}{\mathrm{1}−{xt}}{dt} \\ $$$$\left.\mathrm{3}\right)\:{give}\:{f}^{\left({n}\right)} \left({x}\right)\:{at}\:{form}\:{of}\:{integral} \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\int_{\mathrm{0}}…
Question Number 130214 by Lordose last updated on 23/Jan/21 $$\int\frac{\mathrm{u}^{\mathrm{2}} }{\left(\mathrm{1}+\mathrm{u}^{\mathrm{2}} \right)^{\mathrm{2}} }\mathrm{du} \\ $$ Answered by liberty last updated on 23/Jan/21 $$\mathrm{J}=\int\:\frac{\left(\mathrm{u}^{\mathrm{2}} +\mathrm{1}\right)−\mathrm{1}}{\left(\mathrm{1}+\mathrm{u}^{\mathrm{2}} \right)^{\mathrm{2}}…
Question Number 130208 by liberty last updated on 23/Jan/21 $$\:\mathrm{The}\:\mathrm{loop}\:\mathrm{of}\:\mathrm{curve}\:\mathrm{2ay}^{\mathrm{2}} =\mathrm{x}\left(\mathrm{x}−\mathrm{a}\right)^{\mathrm{2}} \\ $$$$\mathrm{revolves}\:\mathrm{about}\:\mathrm{straight}\:\mathrm{line}\: \\ $$$$\mathrm{y}=\mathrm{a}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{the}\:\mathrm{solid} \\ $$$$\mathrm{generated}. \\ $$ Answered by benjo_mathlover last updated on…
Question Number 130203 by mnjuly1970 last updated on 23/Jan/21 Answered by Dwaipayan Shikari last updated on 23/Jan/21 $${I}\left({a}\right)−{I}\left(\beta\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{{a}} }{\left(\mathrm{1}+{x}\right){logx}}−\frac{{x}^{\beta} }{\left(\mathrm{1}+{x}\right){log}\left({x}\right)}{dx} \\ $$$${I}'\left({a}\right)−{I}'\left(\beta\right)=\underset{{n}=\mathrm{1}} {\overset{\infty}…
Question Number 64662 by aliesam last updated on 20/Jul/19 $$\int\frac{{dx}}{\left({x}^{\mathrm{8}} +{x}^{\mathrm{4}} +\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$ \\ $$$$\int_{\frac{\mathrm{1}}{{x}}} ^{{x}} \frac{{ln}\left({t}\right)}{{t}^{\mathrm{2}} +\mathrm{1}}\:{dt} \\ $$ Commented by MJS…