Question Number 97041 by bemath last updated on 06/Jun/20 $$\int\:\mathrm{sin}\:^{\mathrm{8}} \left({x}\right)\:\mathrm{cos}\:^{\mathrm{8}} \left({x}\right)\:{dx}\:=\:? \\ $$ Answered by john santu last updated on 06/Jun/20 $$\Rightarrow\mathrm{sin}\:^{\mathrm{8}} {x}.\mathrm{cos}\:^{\mathrm{8}} {x}\:=\:\frac{\mathrm{sin}\:^{\mathrm{8}}…
Question Number 31505 by abdo imad last updated on 09/Mar/18 $$\:{find}\:\:\:\:\int_{{a}} ^{{b}} \:\:\:\:\frac{\mathrm{1}−{x}^{\mathrm{2}} }{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\sqrt{\mathrm{1}+{x}^{\mathrm{4}} }}{dx}\:\:{with}\:{a}>\mathrm{1}\:{and}\:{b}>\mathrm{1}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 31503 by abdo imad last updated on 09/Mar/18 $${find}\:\:\int_{\mathrm{2}} ^{\sqrt{\mathrm{5}}} \:\:\:\:\:\frac{{dt}}{{t}\sqrt{{t}^{\mathrm{2}} −\mathrm{1}}}\:. \\ $$ Commented by abdo imad last updated on 16/Mar/18 $${ch}.\:{t}={ch}\left({x}\right)\:{give}\:\:{I}\:=\:\int_{{argch}\left(\mathrm{2}\right)}…
Question Number 31501 by abdo imad last updated on 09/Mar/18 $${find}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left(\mathrm{1}\:+\mathrm{2}{tanx}\right){dx}. \\ $$ Commented by abdo imad last updated on 12/Mar/18 $${let}\:{introduce}\:{f}\left({t}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}}…
Question Number 162575 by Ar Brandon last updated on 30/Dec/21 $$\int_{\mathrm{0}} ^{\pi} \frac{{x}^{\mathrm{2}} }{\mathrm{1}+\mathrm{sin}{x}}{dx} \\ $$ Answered by phanphuoc last updated on 30/Dec/21 $${you}\:{can}\:{put}\:{x}={pi}−{t} \\…
Question Number 97007 by bagjamath last updated on 06/Jun/20 Commented by bagjamath last updated on 06/Jun/20 $${What}\:{is}\:{the}\:{theorm}\:{Sir}? \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} {y}\:{dx}=\int_{\infty} ^{\mathrm{0}} {x}\:{dy}\:?? \\ $$…
Question Number 31466 by abdo imad last updated on 08/Mar/18 $${let}\:{give}\:{I}_{{n}} =\:\int_{\frac{\mathrm{1}}{{n}}} ^{\mathrm{1}} \:\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }\:{dt} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{I}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow\infty} \:{I}_{{n}} \:\:\:. \\ $$ Terms of…
Question Number 31465 by abdo imad last updated on 08/Mar/18 $${find}\:\:{F}\left(\alpha\right)=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{arctan}\left(\alpha{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}\:\:{with}\:\alpha\:\in\:{R}−\left\{\mathrm{1},−\mathrm{1}\right\} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 31464 by abdo imad last updated on 08/Mar/18 $$\left.\mathrm{1}\right)\:{find}\:\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:{e}^{−{x}} {cos}\left({nx}\right){dx} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:{S}_{{n}} =\:\sum_{{k}=\mathrm{0}} ^{{n}} \:{A}_{{k}} \:\:. \\ $$ Terms of…
Question Number 162535 by mnjuly1970 last updated on 30/Dec/21 $$ \\ $$$$\:\:\:\:\:\mathrm{prove}\:\mathrm{that} \\ $$$$\Omega\:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:\:\mathrm{ln}\:\left(\frac{\mathrm{1}}{{x}}\:\right)}{\:{x}^{\:\mathrm{4}} \:+\:\mathrm{17}{x}^{\:\mathrm{2}} \:+\:\mathrm{16}}\:{dx}\overset{?} {=}\:\frac{\pi}{\mathrm{60}}\:\mathrm{ln}\left(\mathrm{2}\right) \\ $$$$ \\ $$ Commented by…