Menu Close

Author: Tinku Tara

0-e-x-2-e-x-2-e-x-2-euler-s-mascheroni-constant-golden-ratio-silver-ratio-klipto-quanta-

Question Number 224197 by klipto last updated on 24/Aug/25 $$\int_{\mathrm{0}} ^{\infty} \left(\boldsymbol{\mathrm{e}}^{−\boldsymbol{\varphi\mathrm{x}}^{\mathrm{2}} } +\boldsymbol{\mathrm{e}}^{−\boldsymbol{\delta\mathrm{x}}^{\mathrm{2}} } +\boldsymbol{\mathrm{e}}^{−\boldsymbol{\gamma\mathrm{x}}^{\mathrm{2}} } \right) \\ $$$$\boldsymbol{\gamma}−\boldsymbol{\mathrm{euler}}'\boldsymbol{\mathrm{s}}\:\boldsymbol{\mathrm{mascheroni}}\:\boldsymbol{\mathrm{constant}} \\ $$$$\boldsymbol{\varphi}−\boldsymbol{\mathrm{golden}}\:\boldsymbol{\mathrm{ratio}} \\ $$$$\boldsymbol{\delta}−\boldsymbol{\mathrm{silver}}\:\boldsymbol{\mathrm{ratio}} \\…

Calculate-I-sin-x-1-sin-x-dx-

Question Number 224182 by CrispyXYZ last updated on 24/Aug/25 $$\mathrm{Calculate} \\ $$$${I}=\int\:\frac{\mathrm{sin}\:{x}}{\mathrm{1}+\:\mathrm{sin}\:{x}}\:\mathrm{d}{x} \\ $$ Answered by Frix last updated on 24/Aug/25 $$\int\frac{\mathrm{sin}\:{x}}{\mathrm{1}+\mathrm{sin}\:{x}}{dx}=\int\frac{\left(\mathrm{1}−\mathrm{sin}\:{x}\right)\mathrm{sin}\:{x}}{\left(\mathrm{1}−\mathrm{sin}\:{x}\right)\left(\mathrm{1}+\mathrm{sin}\:{x}\right)}{dx}= \\ $$$$=\int\frac{\mathrm{sin}\:{x}\:−\mathrm{sin}^{\mathrm{2}} \:{x}}{\mathrm{cos}^{\mathrm{2}}…

Question-224150

Question Number 224150 by behi834171 last updated on 23/Aug/25 Commented by behi834171 last updated on 23/Aug/25 $$\boldsymbol{{x}};\:\boldsymbol{{in}}\:\boldsymbol{{terms}}\:\boldsymbol{{of}}:\:\left(\boldsymbol{{a}}\:\boldsymbol{{and}}\:\boldsymbol{{b}}\right)\in\boldsymbol{{R}} \\ $$ Commented by Ghisom_ last updated on…

Question-224144

Question Number 224144 by mr W last updated on 23/Aug/25 Commented by mr W last updated on 23/Aug/25 $${find}\:{the}\:{normal}\:{force}\:\boldsymbol{{N}}\:{between}\: \\ $$$${two}\:{solid}\:{cylinders}\:{with}\:{masses} \\ $$$$\boldsymbol{{m}}_{\mathrm{1}} ,\:\boldsymbol{{m}}_{\mathrm{2}} \:{and}\:{radii}\:\boldsymbol{{r}}_{\mathrm{1}}…