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Author: Tinku Tara

Question-226339

Question Number 226339 by Spillover last updated on 25/Nov/25 Answered by Ghisom_ last updated on 26/Nov/25 $$=\int\frac{{x}^{\mathrm{5}} }{{x}^{\mathrm{12}} −\mathrm{1}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}={x}^{\mathrm{6}} \right] \\ $$$$=\frac{\mathrm{1}}{\mathrm{6}}\int\frac{{dt}}{{t}^{\mathrm{2}} −\mathrm{1}}=\frac{\mathrm{1}}{\mathrm{12}}\mathrm{ln}\:\frac{{t}−\mathrm{1}}{{t}+\mathrm{1}}\:=…

Question-226173

Question Number 226173 by sonukgindia last updated on 22/Nov/25 Answered by A5T last updated on 22/Nov/25 $$\mathrm{x}^{\mathrm{2013}} +\left(\mathrm{2014}−\mathrm{x}\right)^{\mathrm{2013}} \:\equiv\:\mathrm{x}^{\mathrm{2013}} +\left(−\mathrm{x}\right)^{\mathrm{2013}} \equiv\mathrm{0}\left(\mathrm{mod}\:\mathrm{2014}\right) \\ $$$$\mathrm{1}^{\mathrm{2013}} +\mathrm{2}^{\mathrm{2013}} +\mathrm{3}^{\mathrm{2013}}…