Question Number 79325 by Henri Boucatchou last updated on 24/Jan/20 $$\:\boldsymbol{{Convergence}}\:\:\boldsymbol{{of}}\:: \\ $$$$\left.\:\:\mathrm{1}\right)\:\:\:\boldsymbol{{I}}=\int_{\mathrm{1}} ^{\:\infty} \frac{\boldsymbol{{e}}^{−\boldsymbol{{t}}/\mathrm{5}} \mid\boldsymbol{{sin}}\left(\boldsymbol{{lnt}}\right)\mid}{\left(\boldsymbol{{t}}−\mathrm{1}\right)^{\mathrm{3}/\mathrm{2}} }\boldsymbol{{dt}} \\ $$$$\left.\:\:\mathrm{2}\right)\:\:\:\boldsymbol{{I}}=\int_{\mathrm{1}} ^{\infty} \frac{\sqrt{\boldsymbol{{lnx}}}}{\left(\boldsymbol{{x}}−\mathrm{1}\right)\sqrt{\boldsymbol{{x}}}}\boldsymbol{{dx}} \\ $$ Commented by…
Question Number 144813 by mnjuly1970 last updated on 29/Jun/21 $$ \\ $$$$\:\:\:\:\:\:\mathrm{I}:=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{ln}\:\left({x}\right)}{\mathrm{1}\:+\:{x}^{\:\mathrm{2}} }\:{dx} \\ $$$$\:\:\:\:\:\:\:\:\::=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \mathrm{ln}\left({x}\:\right)\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{\:{n}} \:{x}^{\:\mathrm{2}{n}} \:{dx} \\ $$$$\:\:\:\:\:\:\:\::=\:\underset{{n}=\mathrm{0}}…
Question Number 144815 by mnjuly1970 last updated on 29/Jun/21 Answered by mindispower last updated on 30/Jun/21 $$=\int_{\mathrm{0}} ^{\infty} \frac{{sin}\left({x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right)+{sin}\left(\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }−{x}\right)}{\mathrm{2}\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:}{dx} \\ $$$${x}={sh}\left({t}\right) \\…
Question Number 144811 by kayuspride last updated on 29/Jun/21 $$\int\left\{\frac{\mathrm{3}}{\:\sqrt{{x}^{\mathrm{2}} −{tan}^{\mathrm{2}} {x}}}\right\}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 144792 by imjagoll last updated on 29/Jun/21 $$\:\int\:\frac{\mathrm{2x}^{\mathrm{3}} −\mathrm{1}}{\mathrm{x}^{\mathrm{4}} +\mathrm{x}}\:\mathrm{dx}\:? \\ $$ Answered by liberty last updated on 29/Jun/21 $$\:\Omega=\int\:\frac{\mathrm{2x}^{\mathrm{3}} −\mathrm{1}}{\mathrm{x}^{\mathrm{4}} +\mathrm{x}}\:\mathrm{dx}\:=\:\int\:\frac{\mathrm{2x}−\mathrm{x}^{−\mathrm{2}} }{\mathrm{x}^{\mathrm{2}}…
Question Number 144789 by Nono last updated on 29/Jun/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 144788 by nonh1 last updated on 29/Jun/21 Answered by gsk2684 last updated on 30/Jun/21 $$\underset{\mathrm{x}=\mathrm{0}} {\overset{\mathrm{1}} {\int}}\left(\underset{\mathrm{y}=−\mathrm{3}} {\overset{\mathrm{3}} {\int}}\left(\mathrm{4}−\mathrm{y}^{\mathrm{2}} \right)\mathrm{dy}\right)\:\mathrm{dx} \\ $$$$\underset{\mathrm{0}} {\overset{\mathrm{1}}…
Question Number 144787 by mnjuly1970 last updated on 29/Jun/21 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{Q}\:::\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:#\:\mathrm{Calculus}\:# \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{If}\::\:\:\:\:\:\:\:\:\boldsymbol{\phi}\:\left(\:{n}\:\right)\::\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{x}^{\:\mathrm{2}{n}} }{\mathrm{1}\:+\:{x}^{\:\mathrm{2}} }\:\mathrm{d}{x}\: \\ $$$$\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{then}\:\:\mathrm{find}\:\:\mathrm{the}\:\:\mathrm{value}\:\mathrm{of}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\…
Question Number 144782 by nonh1 last updated on 29/Jun/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 13705 by ajfour last updated on 22/May/17 $${Assuming}\:{no}\:{air}\:{resistance}, \\ $$$${and}\:{angle}\:{of}\:{projection}\:\alpha=\frac{\pi}{\mathrm{4}}\:, \\ $$$${find}\:{the}\:{ratio}\:{of}\:{the}\:{length}\:{of} \\ $$$${trajectory}\:\boldsymbol{{L}}\:{of}\:{a}\:{projectile}\:{motion}\: \\ $$$$\left({by}\:{the}\:{time}\:{it}\:{hits}\:{the}\:{ground}\right) \\ $$$${to}\:{its}\:{horizontal}\:{range}\:\boldsymbol{{R}}\:{on}\: \\ $$$${ground}.\:\:\:\:\:\:\frac{\boldsymbol{{L}}}{\boldsymbol{{R}}}=? \\ $$ Commented…