Question Number 76052 by Ajao yinka last updated on 23/Dec/19 Commented by MJS last updated on 23/Dec/19 $${t}=\mathrm{e}^{−{x}} \:\rightarrow\:{dx}=−\mathrm{e}^{{x}} {dt} \\ $$$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{t}^{−{t}} {dt}\approx\mathrm{1}.\mathrm{291286}…
Question Number 76053 by john santuy last updated on 23/Dec/19 $${how}\:{I}\:{calculate}\:\int\frac{\mathrm{1}}{{x}^{\mathrm{8}} +{x}^{\mathrm{2}} }{dx}\:? \\ $$ Commented by abdomathmax last updated on 23/Dec/19 $${decompose}\:{the}\:{fraction}\:{F}\left({x}\right)=\frac{\mathrm{1}}{{x}^{\mathrm{2}} +{x}^{\mathrm{8}} }\:\:{and}\:{see}…
Question Number 141581 by qaz last updated on 20/May/21 $$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{{n}} }{\mathrm{1}+{x}}{dx}=? \\ $$ Commented by Dwaipayan Shikari last updated on 20/May/21…
Question Number 141577 by qaz last updated on 20/May/21 $$\left(\frac{\mathrm{1}}{\mathrm{1}\centerdot\mathrm{2}\centerdot\mathrm{3}}\right)^{\mathrm{2}} +\left(\frac{\mathrm{1}}{\mathrm{2}\centerdot\mathrm{3}\centerdot\mathrm{4}}\right)^{\mathrm{2}} +\left(\frac{\mathrm{1}}{\mathrm{3}\centerdot\mathrm{4}\centerdot\mathrm{5}}\right)^{\mathrm{2}} +…=\frac{\mathrm{1}}{\mathrm{16}}\left(\mathrm{4}\pi^{\mathrm{2}} −\mathrm{39}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 10510 by ajfour last updated on 15/Feb/17 Answered by mrW1 last updated on 15/Feb/17 $$\mathrm{2sin}\:{x}+\mathrm{3cos}\:{x} \\ $$$$=\sqrt{\mathrm{13}}×\left(\frac{\mathrm{2}}{\:\sqrt{\mathrm{13}}}\mathrm{sin}\:{x}+\frac{\mathrm{3}}{\:\sqrt{\mathrm{13}}}\mathrm{cos}\:{x}\right) \\ $$$$=\sqrt{\mathrm{13}}×\left(\mathrm{sin}\:{x}\mathrm{cos}\:{t}+\mathrm{cos}\:{x}\mathrm{sin}\:{t}\right) \\ $$$$=\sqrt{\mathrm{13}}×\mathrm{sin}\:\left({x}+{t}\right) \\ $$$${with}\:{t}=\mathrm{sin}^{−\mathrm{1}}…
Question Number 10495 by ajfour last updated on 14/Feb/17 $$\int_{\mathrm{0}} ^{\mathrm{2}\pi} \sqrt{{R}^{\mathrm{2}} +{r}^{\mathrm{2}} −\mathrm{2}{Rr}\mathrm{cos}\:\theta}\:{d}\theta \\ $$ Answered by robocop last updated on 14/Feb/17 $${todo}\:{en}\:{funcion}\:{de}\:\theta \\…
Question Number 141560 by mnjuly1970 last updated on 20/May/21 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:……..{Nice}\:….{Calculus}\left({I}\right)…… \\ $$$$\:\:\:\:\:{Evaluate}::\:\: \\ $$$$\:\:\:\:\:\mathrm{I}:=\int_{\mathrm{0}} ^{\:{ln}\left(\mathrm{2}\right)} \frac{{x}}{{e}^{{x}} +\mathrm{2}{e}^{−{x}} −\mathrm{2}}{dx}=? \\ $$$$\:\:\:\:…… \\ $$ Answered…
Question Number 76014 by Master last updated on 22/Dec/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 76015 by Master last updated on 22/Dec/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 10469 by FilupSmith last updated on 11/Feb/17 $$\mathrm{One}\:\mathrm{definition}\:\mathrm{of}\:\:\Gamma\left({x}+\mathrm{1}\right)\:\:\mathrm{is}: \\ $$$$\Gamma\left({x}+\mathrm{1}\right)=\int_{\mathrm{0}} ^{\:\infty} {e}^{−{t}} {t}^{{x}} {dx} \\ $$$$\: \\ $$$$\mathrm{According}\:\mathrm{to}\:\mathrm{WolframAlpha},\:\mathrm{another} \\ $$$$\mathrm{definition}\:\mathrm{is}: \\ $$$$\Gamma\left({x}+\mathrm{1}\right)=\frac{\mathrm{1}}{{e}^{\mathrm{2}{i}\pi{x}} −\mathrm{1}}\oint_{{L}}…