Question Number 81888 by rajesh4661kumar@gmail.com last updated on 16/Feb/20 Commented by mathmax by abdo last updated on 16/Feb/20 $${let}\:{A}\:=\int\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}\:\:{we}\:{do}\:{the}\:{changement}\:{x}\:={cht}\:\Rightarrow \\ $$$${A}\:=\int\:\:\:\frac{{sht}\:{dt}}{\left({ch}^{\mathrm{2}} {t}\:+\mathrm{1}\right){sht}}\:=\int\:\:\frac{{dt}}{\mathrm{1}+\frac{\mathrm{1}+{ch}\left(\mathrm{2}{t}\right)}{\mathrm{2}}}\:=\int\:\:\frac{\mathrm{2}{dt}}{\mathrm{3}+{ch}\left(\mathrm{2}{t}\right)} \\…
Question Number 147399 by ArielVyny last updated on 20/Jul/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{e}^{\mathrm{2}{arctg}\left({u}\right)} }{\:\sqrt{{u}}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 81801 by Power last updated on 15/Feb/20 Commented by mathmax by abdo last updated on 16/Feb/20 $${changement}\:{x}^{{n}} \:={cos}^{\mathrm{2}} {t}\:{give}\:{x}\:=\left({cost}\right)^{\frac{\mathrm{2}}{{n}}} \:\Rightarrow{dx}\:=−\frac{\mathrm{2}}{{n}}{sint}\:\left({cost}\right)^{\frac{\mathrm{2}}{{n}}−\mathrm{1}} \\ $$$$\Rightarrow\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 147309 by puissant last updated on 19/Jul/21 Answered by mathmax by abdo last updated on 19/Jul/21 $$\mathrm{I}=\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{cosx}}{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} }\:\Rightarrow\mathrm{2I}=\int_{−\infty} ^{+\infty} \:\frac{\mathrm{cosx}}{\left(\mathrm{x}^{\mathrm{2}}…
Question Number 16240 by tawa tawa last updated on 19/Jun/17 Commented by tawa tawa last updated on 19/Jun/17 $$\mathrm{please}\:\mathrm{help}. \\ $$ Answered by ajfour last…
Question Number 147310 by mnjuly1970 last updated on 19/Jul/21 Commented by Tawa11 last updated on 03/Aug/21 $$\mathrm{Great} \\ $$ Answered by qaz last updated on…
Question Number 147287 by mnjuly1970 last updated on 19/Jul/21 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:…\mathrm{Advanced}\:\:\mathrm{Calculus}… \\ $$$$ \\ $$$$\:\:\:\:\:\:\mathrm{C}{alculate}\:::\:\:\:\:\begin{cases}{\:\:\mathrm{i}\:::\:\:\:\:\:\:\mathrm{I}\::=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \mathrm{ln}\left(\mathrm{x}\right).\mathrm{ln}\left(\mathrm{1}+\mathrm{x}\right)\:\mathrm{dx}}\\{\:\:\mathrm{ii}\:::\:\:\:\:\:\mathrm{J}\::=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \mathrm{Li}_{\:\mathrm{2}} \left(\:\mathrm{1}−\:\mathrm{x}^{\:\mathrm{2}} \right)\:=?}\end{cases} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{Note}::\:\:\:\mathrm{Li}_{\mathrm{2}} \:\left(\mathrm{x}\right)\:=\:\underset{{n}=\mathrm{1}}…
Question Number 81739 by TANMAY PANACEA last updated on 15/Feb/20 $$\int\frac{{dx}}{{cos}^{\mathrm{3}} {x}−{sin}^{\mathrm{3}} {x}} \\ $$ Commented by abdomathmax last updated on 16/Feb/20 $${I}\:=\int\:\:\frac{{dx}}{{cos}^{\mathrm{3}} {x}−{sin}^{\mathrm{3}} {x}}\:=\int\:\frac{{dx}}{\left({cosx}−{sinx}\right)\left({cos}^{\mathrm{2}}…
Question Number 147275 by ArielVyny last updated on 19/Jul/21 $${f}\left({x}\right)=\int_{\mathrm{0}} ^{{x}} {e}^{{t}−\frac{{t}^{\mathrm{2}} }{\mathrm{2}}} {dt}\: \\ $$$${show}\:{that}\:\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({t}\right){dt}=\sqrt{{e}}−\mathrm{1} \\ $$ Answered by mindispower last updated…
Question Number 81719 by mathmax by abdo last updated on 14/Feb/20 $$\left.\mathrm{1}\right)\:{find}\:\int\:\:\:\frac{{dx}}{\left({x}+\mathrm{2}\right)^{\mathrm{5}} \left({x}−\mathrm{3}\right)^{\mathrm{9}} } \\ $$$$ \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{4}} ^{+\infty} \:\frac{{dx}}{\left({x}+\mathrm{2}\right)^{\mathrm{5}} \left({x}−\mathrm{3}\right)^{\mathrm{9}} } \\ $$ Commented…