Question Number 66339 by mathmax by abdo last updated on 12/Aug/19 $${calculate}\:\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{1}} \:\frac{{dx}}{\:\sqrt{\mathrm{4}{x}^{\mathrm{2}} −\mathrm{1}}+\sqrt{\mathrm{4}{x}^{\mathrm{2}} \:+\mathrm{1}}} \\ $$ Commented by Prithwish sen last updated on…
Question Number 131875 by mnjuly1970 last updated on 09/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:\:{calculus}.. \\ $$$$\:\:\:\:\:\Phi=\int_{\mathrm{0}} ^{\:\infty} \frac{{ln}\left({cosh}\left({x}\right)\right)}{{cosh}\left({x}\right)}{dx}=??? \\ $$ Answered by mindispower last updated on 09/Feb/21 $$=\int_{\mathrm{1}} ^{\infty}…
Question Number 66336 by mathmax by abdo last updated on 12/Aug/19 $${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{tanx}}{\:\sqrt{\mathrm{2}}{cosx}\:+\mathrm{2}{sin}^{\mathrm{2}} {x}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 131874 by mnjuly1970 last updated on 09/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{calculus}\:… \\ $$$$\:\:\:\phi\:=\int_{\mathrm{0}} ^{\:\infty} \frac{{tanh}^{\mathrm{2}} \left({x}\right){dx}}{{x}^{\mathrm{2}} }\:=? \\ $$$$ \\ $$ Terms of Service Privacy Policy…
Question Number 66337 by mathmax by abdo last updated on 12/Aug/19 $${calculate}\:\int_{−\mathrm{7}} ^{−\mathrm{3}} \:\:\frac{\left({x}−\mathrm{1}\right){dx}}{\:\sqrt{{x}^{\mathrm{2}} \:+\mathrm{2}{x}−\mathrm{3}}} \\ $$ Commented by Prithwish sen last updated on 13/Aug/19…
Question Number 800 by 123456 last updated on 15/Mar/15 $$\underset{{n}=\mathrm{0}} {\overset{+\infty} {\sum}}\frac{{n}\centerdot\mathrm{cos}\left(\frac{{n}}{\pi^{{n}} }\right)}{\mathrm{1}+{n}^{\mathrm{2}} }\:{converge}\:{ou}\:{diverge}? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 66334 by mathmax by abdo last updated on 12/Aug/19 $${let}\:{I}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:{e}^{−\mathrm{2}{t}} \:{cos}^{\mathrm{4}} {t}\:{dt}\:{and}\:{J}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{e}^{−\mathrm{2}{t}} \:{sin}^{\mathrm{4}} {tdt} \\ $$$$\left.\mathrm{1}\right){calculate}\:\:{I}+{J}\:{and}\:{I}−{J} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:{I}\:{and}\:{J}. \\…
Question Number 799 by 123456 last updated on 15/Mar/15 $$\underset{\mathrm{0}} {\overset{\pi} {\int}}\mathrm{sin}\:{x}\:\mathrm{ln}\:\left(\mathrm{1}−\mathrm{cos}\:{x}\right){dx}\:{converge}? \\ $$ Answered by prakash jain last updated on 15/Mar/15 $$\mathrm{1}−\mathrm{cos}\:{x}={t} \\ $$$${x}=\mathrm{0}\Rightarrow{t}=\mathrm{0}…
Question Number 66335 by mathmax by abdo last updated on 12/Aug/19 $${find}\:\:\int_{−\frac{\pi}{\mathrm{6}}} ^{\frac{\pi}{\mathrm{6}}} \:\frac{\mathrm{1}+{tanx}}{\mathrm{1}+{sin}\left(\mathrm{2}{x}\right)}{dx} \\ $$ Commented by Prithwish sen last updated on 13/Aug/19 $$\int_{−\frac{\pi}{\mathrm{6}}}…
Question Number 798 by 123456 last updated on 15/Mar/15 $$\sqrt{\mathrm{1}+\mathrm{2}\sqrt{\mathrm{1}+\mathrm{3}\sqrt{\mathrm{1}+\mathrm{4}\sqrt{\mathrm{1}+\centerdot\centerdot\centerdot}}}} \\ $$ Answered by prakash jain last updated on 15/Mar/15 $$\mathrm{Ramanujan}'{s}\:\mathrm{Formula} \\ $$$${x}+\mathrm{1}=\sqrt{\mathrm{1}+{x}\sqrt{\mathrm{1}+\left({x}+\mathrm{1}\right)\sqrt{\mathrm{1}+\left({x}+\mathrm{2}\right)\sqrt{\mathrm{1}+…}}}} \\ $$$$\mathrm{For}\:{x}=\mathrm{2}…