Question Number 65676 by mathmax by abdo last updated on 01/Aug/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{x}^{\mathrm{2}} −\frac{\mathrm{1}}{{x}^{\mathrm{2}} }} {dx} \\ $$ Commented by ~ À ® @…
Question Number 131211 by mnjuly1970 last updated on 02/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:…{calculus}… \\ $$$$\:{prove}\:{that}:: \\ $$$$\:\boldsymbol{\Phi}=\int_{\mathrm{0}} ^{\:\frac{\boldsymbol{\pi}}{\mathrm{4}}} \left(\frac{\sqrt{\boldsymbol{{tan}}\left(\boldsymbol{{x}}\right)+\boldsymbol{{tan}}^{\mathrm{2}} \left(\boldsymbol{{x}}\right)}}{\:\sqrt{\boldsymbol{{tan}}\left(\boldsymbol{{x}}\right)−\boldsymbol{{tan}}^{\mathrm{2}} \left(\boldsymbol{{x}}\right)}}\:\boldsymbol{{sin}}\left(\boldsymbol{{x}}\right)\right)\boldsymbol{{dx}}\: \\ $$$$\:\:\:\:=\frac{\mathrm{1}}{\mathrm{2}}+\frac{\sqrt{\boldsymbol{\pi}}}{\mathrm{8}}\:\left(\frac{\boldsymbol{\Gamma}\left(\frac{\mathrm{1}}{\mathrm{4}}\right)}{\boldsymbol{\Gamma}\left(\frac{\mathrm{3}}{\mathrm{4}}\right)}−\frac{\boldsymbol{\Gamma}\left(\frac{\mathrm{3}}{\mathrm{4}}\right)}{\boldsymbol{\Gamma}\left(\frac{\mathrm{5}}{\mathrm{4}}\right)}\right) \\ $$ Answered by Ar…
Question Number 65675 by mathmax by abdo last updated on 01/Aug/19 $$\left.\mathrm{1}\right)\:{find}\:\int\:\frac{{dx}}{\:\sqrt{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}−\mathrm{2}\right)}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 133 by sagarwal last updated on 25/Jan/15 $$\mathrm{Evaluate}\:\int\sqrt{\mathrm{sin}\:{x}}{dx} \\ $$ Answered by gkfichadia last updated on 10/Dec/14 $$ \\ $$$$ \\ $$$$ \\…
Question Number 65665 by mathmax by abdo last updated on 01/Aug/19 $${calculate}\:\int_{−\mathrm{2}} ^{+\infty} \:\:\frac{{e}^{−{x}} }{\:\sqrt{{x}+\mathrm{2}}}\:{dx} \\ $$$$ \\ $$ Commented by mathmax by abdo last…
Question Number 131189 by Raxreedoroid last updated on 02/Feb/21 $$\int\frac{−{sin}\left({ln}\left({k}^{{x}} \right)\right)}{\:\sqrt{{k}}}{dx}=?? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 131187 by mnjuly1970 last updated on 02/Feb/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 131183 by john_santu last updated on 02/Feb/21 Answered by liberty last updated on 02/Feb/21 $$\:\frac{\mathrm{dP}}{\left(\mathrm{32}−\mathrm{P}\right)\mathrm{P}}\:=\:\mathrm{0}.\mathrm{0015}\:\mathrm{dt}\: \\ $$$$\frac{\mathrm{1}}{\mathrm{32}}\:\int\:\left[\:\frac{\mathrm{1}}{\mathrm{32}−\mathrm{P}}\:+\frac{\mathrm{1}}{\mathrm{P}}\:\right]\mathrm{dP}\:=\:\int\mathrm{0}.\mathrm{0015}\:\mathrm{dt} \\ $$$$\frac{\mathrm{1}}{\mathrm{32}}\:\mathrm{ln}\:\mid\frac{\mathrm{P}}{\mathrm{32}−\mathrm{P}}\:\mid\:=\:\mathrm{0}.\mathrm{0015t}\:+\:\mathrm{c}\: \\ $$$$\mathrm{ln}\:\mid\frac{\mathrm{P}}{\mathrm{32}−\mathrm{P}}\mid\:=\:\mathrm{0}.\mathrm{48t}+\mathrm{C}\:;\:\frac{\mathrm{P}\left(\mathrm{t}\right)}{\mathrm{32}−\mathrm{P}\left(\mathrm{t}\right)}\:=\:\lambda\mathrm{e}^{\mathrm{0}.\mathrm{048t}} \\ $$$$\Leftrightarrow\:\frac{\mathrm{32}−\mathrm{P}\left(\mathrm{t}\right)}{\mathrm{P}\left(\mathrm{t}\right)}\:=\:\frac{\mathrm{1}}{\lambda}\mathrm{e}^{−\mathrm{0}.\mathrm{048t}}…
Question Number 131176 by Raxreedoroid last updated on 02/Feb/21 $$\int\frac{{cos}\left({ln}\left({a}^{{x}} \right)\right)}{\:\sqrt{{k}}}{dx}=?? \\ $$ Answered by Ar Brandon last updated on 02/Feb/21 $$\mathrm{I}=\int\frac{\mathrm{cos}\left(\mathrm{lna}^{\mathrm{x}} \right)}{\:\sqrt{\mathrm{k}}}\mathrm{dx}\:,\:\mathrm{t}=\mathrm{lna}^{\mathrm{x}} \:\Rightarrow\mathrm{dt}=\mathrm{lnadx} \\…
Question Number 131167 by 676597498 last updated on 02/Feb/21 Answered by SEKRET last updated on 02/Feb/21 $$\boldsymbol{\mathrm{U}}_{\boldsymbol{\mathrm{n}}} =\left(\mathrm{1}+\frac{\mathrm{1}}{\boldsymbol{\mathrm{n}}^{\mathrm{2}} }\right)\left(\mathrm{1}+\frac{\mathrm{2}}{\boldsymbol{\mathrm{n}}^{\mathrm{2}} }\right)….\left(\mathrm{1}+\frac{\boldsymbol{\mathrm{n}}}{\boldsymbol{\mathrm{n}}^{\mathrm{2}} }\right) \\ $$$$\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{U}}_{\boldsymbol{\mathrm{n}}} \right)=\:\boldsymbol{\mathrm{ln}}\left(\mathrm{1}+\frac{\mathrm{1}}{\boldsymbol{\mathrm{n}}^{\mathrm{2}} }\right)+\boldsymbol{\mathrm{ln}}\left(\mathrm{1}+\frac{\mathrm{2}}{\:\:\boldsymbol{\mathrm{n}}^{\mathrm{2}}…