Question Number 153759 by mnjuly1970 last updated on 10/Sep/21 $$ \\ $$$$\Omega=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left\{{n}^{\mathrm{2}} \left(\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{\:{sin}^{\:\mathrm{2}} \left({x}\:\right)}{\left({sin}\left({x}\right)+{cos}\left({x}\right)\right)^{\:\mathrm{4}} }\right)^{\:{n}} {dx}\right\}=? \\ $$$$ \\ $$ Terms…
Question Number 22678 by tawa tawa last updated on 21/Oct/17 $$\int\:\frac{\mathrm{9x}^{\mathrm{4}} \:+\:\mathrm{12x}\left(\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{1}\right)}{\mathrm{2}\left(\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{1}\right)^{\mathrm{1}/\mathrm{2}} }\:\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 88206 by jagoll last updated on 09/Apr/20 $$\int\:\:\frac{\mathrm{x}+\mathrm{x}^{\mathrm{3}} }{\mathrm{1}+\mathrm{x}^{\mathrm{4}} }\:\mathrm{dx}\: \\ $$ Answered by john santu last updated on 09/Apr/20 $$=\:\int\:\frac{{x}}{\mathrm{1}+{x}^{\mathrm{4}} }\:{dx}\:+\:\int\:\frac{{x}^{\mathrm{3}} }{\mathrm{1}+{x}^{\mathrm{4}}…
Question Number 88196 by M±th+et£s last updated on 08/Apr/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 88194 by M±th+et£s last updated on 08/Apr/20 $${find}\:\int\frac{\mathrm{1}}{\:\sqrt{{x}}+\sqrt{{x}+\mathrm{1}}+\sqrt{{x}+\mathrm{2}}}\:{dx} \\ $$$$ \\ $$ Commented by TANMAY PANACEA. last updated on 08/Apr/20 $${excellent}\:{problem}…{thinking} \\ $$…
Question Number 88197 by M±th+et£s last updated on 08/Apr/20 $${prove}\:{that}\: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\frac{{x}^{\mathrm{2}} −\mathrm{2}}{{x}^{\mathrm{2}} −\mathrm{1}}\:}{dx}=\frac{\pi\sqrt{\mathrm{2}\pi}}{\Gamma^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{4}}\right)}+\frac{\Gamma^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{4}}\right)}{\mathrm{4}\sqrt{\mathrm{2}\pi}} \\ $$ Terms of Service Privacy Policy…
Question Number 153734 by mnjuly1970 last updated on 09/Sep/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 153721 by mnjuly1970 last updated on 09/Sep/21 $$ \\ $$$$\:\:\:\:\:\mathrm{prove}\:\:\mathrm{that}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:{x}^{\:\mathrm{3}} }{{sinh}\:\left(\:{x}\:\right)}\:{dx}\:=\:\frac{\pi\:^{\mathrm{4}} }{\mathrm{8}}\:\:\:\:\:\:\:\:\:\:\blacksquare\:{m}.{n}\:\:\:\:\:\:\:\: \\ $$$$ \\ $$ Answered…
Question Number 88181 by ubaydulla last updated on 08/Apr/20 Commented by mathmax by abdo last updated on 09/Apr/20 $$\left.\mathrm{5}\right)\:{y}^{'} \:+{y}\:={e}^{\mathrm{2}{x}} \:\:\:\left({he}\right)\rightarrow{y}^{'} \:+{y}\:=\mathrm{0}\Rightarrow\frac{{y}^{'} }{{y}}=−\mathrm{1}\:\Rightarrow{ln}\mid{y}\mid=−{x}\:+{c}\:\Rightarrow \\ $$$${y}\:={k}\:{e}^{−{x}}…
Question Number 88177 by M±th+et£s last updated on 08/Apr/20 $${prove}\:{that} \\ $$$$ \\ $$$$\int_{\mathrm{0}} ^{\mathrm{2020}} \left({x}−\left[{x}\right]\right)\sqrt{{x}−\left[{x}\right]}\:{dx}=\mathrm{808} \\ $$ Answered by TANMAY PANACEA. last updated on…