Menu Close

Author: Tinku Tara

Question-214916

Question Number 214916 by Spillover last updated on 23/Dec/24 Answered by A5T last updated on 23/Dec/24 $$\mathrm{2017}^{\mathrm{2017}^{\mathrm{2017}} } \equiv\mathrm{1}^{\mathrm{2017}^{\mathrm{2017}} } =\mathrm{1}\left({mod}\:\mathrm{16}\right) \\ $$$$\mathrm{2017}^{\mathrm{2017}^{\mathrm{2017}} } \equiv\mathrm{142}^{\mathrm{2017}^{\mathrm{2017}}…

Question-214915

Question Number 214915 by Spillover last updated on 23/Dec/24 Answered by maths2 last updated on 23/Dec/24 $${x}\rightarrow\mathrm{1}−{x};{Let}\:{A}\:{bee}\:{the}\:{integral} \\ $$$$=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{dx}}{\left(\mathrm{1}+{e}^{−\mathrm{2}+\mathrm{4}{x}} \right)\left(\mathrm{5}+\mathrm{2}{x}−\mathrm{2}{x}^{\mathrm{2}} \right)}\Rightarrow \\ $$$$\mathrm{2}{A}=\int_{\mathrm{0}}…

Question-214876

Question Number 214876 by mr W last updated on 22/Dec/24 Commented by TonyCWX08 last updated on 22/Dec/24 $${Want}\:{a}\:{clarification} \\ $$$${Does}\:{the}\:{tangent}\:{point}\:{at}\:{Blue}\:{circle}\:{cuts}\:{the}\:{line}\:{into}\:\mathrm{2}\:{equal}\:{parts}? \\ $$$${If}\:{no},\:{then}\:{I}\:{have}\:{no}\:{idea}. \\ $$ Commented…

Question-214888

Question Number 214888 by Emmanuel07 last updated on 22/Dec/24 Commented by mr W last updated on 23/Dec/24 $${i}\:{got} \\ $$$${a}_{{n}} =\mathrm{cot}\:\left\{\left[\frac{\mathrm{1}}{\:\sqrt{\mathrm{5}}}\left(\mathrm{tan}^{−\mathrm{1}} \mathrm{2}−\frac{\mathrm{3}\pi}{\mathrm{8}}\right)+\frac{\pi}{\mathrm{8}}\right]\left(\frac{\mathrm{1}−\sqrt{\mathrm{5}}}{\mathrm{2}}\right)^{{n}} −\left[\frac{\mathrm{1}}{\:\sqrt{\mathrm{5}}}\left(\mathrm{tan}^{−\mathrm{1}} \mathrm{2}−\frac{\mathrm{3}\pi}{\mathrm{8}}\right)−\frac{\pi}{\mathrm{8}}\right]\left(\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}\right)^{{n}} \right\}…

0-1-ln-x-ln-1-x-ln-1-x-dx-

Question Number 214857 by MrGaster last updated on 21/Dec/24 $$\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{ln}\left({x}\right)\mathrm{ln}\left(\mathrm{1}+{x}\right)\mathrm{ln}\left(\mathrm{1}−{x}\right){dx}=? \\ $$ Answered by MathematicalUser2357 last updated on 22/Dec/24 $$\boldsymbol{\mathrm{Wait}}…\:\mathrm{They}\:\mathrm{don}'\mathrm{t}\:\mathrm{integrate}\:\mathrm{it}\:\mathrm{like}\:\mathrm{I}\:\mathrm{integrate}\:\mathrm{it}… \\ $$$$\mathrm{0}.\mathrm{139326}… \\…