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Author: Tinku Tara

if-x-R-prove-that-x-6-x-1-gt-0-

Question Number 151475 by mathdanisur last updated on 21/Aug/21 $$\mathrm{if}\:\:\boldsymbol{\mathrm{x}}\in\mathbb{R}\:\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\mathrm{x}^{\mathrm{6}} \:-\:\mathrm{x}\:+\:\mathrm{1}\:>\:\mathrm{0} \\ $$ Answered by dumitrel last updated on 21/Aug/21 $${I}.\:{if}\:{x}\leqslant\mathrm{0}\nRightarrow−{x}\geqslant\mathrm{0};\:{x}^{\mathrm{6}} +\mathrm{1}>\mathrm{0}\Rightarrow \\…

xdx-x-4-4x-2-5-

Question Number 151461 by peter frank last updated on 21/Aug/21 $$\int\frac{\mathrm{xdx}}{\mathrm{x}^{\mathrm{4}} +\mathrm{4x}^{\mathrm{2}} +\mathrm{5}} \\ $$ Answered by puissant last updated on 30/Aug/21 $${I}=\int\frac{{x}}{{x}^{\mathrm{4}} +\mathrm{4}{x}^{\mathrm{2}} +\mathrm{5}}{dx}=\int\frac{{x}}{\left({x}^{\mathrm{2}}…

if-f-x-x-2-2x-2-and-g-x-x-1-find-f-o-g-x-

Question Number 151460 by mathdanisur last updated on 21/Aug/21 $$\mathrm{if}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{2x}\:+\:\mathrm{2} \\ $$$$\mathrm{and}\:\:\mathrm{g}\left(\mathrm{x}\right)\:=\:\sqrt{\mathrm{x}}\:+\:\mathrm{1} \\ $$$$\mathrm{find}\:\:\:\left[\:\mathrm{f}\:{o}\:\mathrm{g}\:\right]\:\left(\mathrm{x}\right)\:=\:? \\ $$ Answered by puissant last updated on 21/Aug/21 $${f}\left({x}\right)={x}^{\mathrm{2}}…

sin-5-xdx-

Question Number 20390 by tammi last updated on 26/Aug/17 $$\int\mathrm{sin}\:^{\mathrm{5}} {xdx} \\ $$ Answered by ajfour last updated on 26/Aug/17 $$\int\left(\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} {x}\right)^{\mathrm{2}} \mathrm{sin}\:{x}\:{dx} \\ $$$${let}\:\mathrm{cos}\:{x}={t}\:\:\Rightarrow\:\:\:−\mathrm{sin}\:{xdx}={dt}…

sin-4-xdx-

Question Number 20389 by tammi last updated on 26/Aug/17 $$\int\mathrm{sin}\:^{\mathrm{4}} {xdx} \\ $$ Answered by Joel577 last updated on 26/Aug/17 $${I}\:=\:\int\:\left(\frac{\mathrm{1}\:−\:\mathrm{cos}\:\mathrm{2}{x}}{\mathrm{2}}\right)^{\mathrm{2}} \:{dx} \\ $$$$\:\:\:\:=\:\frac{\mathrm{1}}{\mathrm{4}}\:\int\:\left(\mathrm{1}\:−\:\mathrm{2cos}\:\mathrm{2}{x}\:+\:\mathrm{cos}^{\mathrm{2}} \:\mathrm{2}{x}\right)\:{dx}…