Question Number 64762 by Lontum Hans-Sandys last updated on 21/Jul/19 $$\mathrm{Given}\:\mathrm{that}\:\mathrm{g}\left(\mathrm{x}\right)=\frac{\mathrm{2}}{\left(\mathrm{1}+\mathrm{x}\right)\left(\mathrm{1}+\mathrm{3x}^{\mathrm{2}} \right.} \\ $$$$\left.\mathrm{a}\right)\:\mathrm{express}\:\mathrm{g}\left(\mathrm{x}\right)\:\mathrm{in}\:\mathrm{partial}\:\mathrm{fractions}. \\ $$$$\left.\mathrm{b}\right)\:\mathrm{evaluate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{g}\left(\left(\mathrm{x}\right)\:\mathrm{dx}.\right. \\ $$ Commented by mathmax by abdo…
Question Number 130296 by sumit Singh last updated on 24/Jan/21 $$\int\left({x}^{\mathrm{2}} /\mathrm{2}+{x}\right){dx} \\ $$ Commented by EDWIN88 last updated on 24/Jan/21 $$\int\:\left(\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}}+\mathrm{x}\right)\mathrm{dx}\:\mathrm{or}\:\int\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}+\mathrm{x}}\:\mathrm{dx}\:? \\…
Question Number 64759 by aliesam last updated on 21/Jul/19 $$\int\frac{{ln}\left({ln}\left({x}\right)\right)}{\left({ln}\left({x}\right)\right)^{{n}} }\:{dx}\:\:\:,\:\:\:{n}\neq\mathrm{1} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 130285 by Lordose last updated on 23/Jan/21 Answered by Olaf last updated on 24/Jan/21 $$\Omega\:=\:\int_{\mathrm{2}} ^{\mathrm{6}} \underset{{k}=\mathrm{1}} {\overset{\mathrm{9}} {\prod}}\left({x}−{k}\right){dx} \\ $$$$\mathrm{Let}\:{u}\:=\:{x}−\mathrm{5} \\ $$$$\Omega\:=\:\int_{−\mathrm{3}}…
Question Number 64745 by mathmax by abdo last updated on 21/Jul/19 $${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}}…