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Question Number 69894 by Rio Michael last updated on 28/Sep/19 $$\int\:\frac{\mathrm{2}{x}^{\mathrm{5}} −{x}}{{x}^{\mathrm{3}} −\mathrm{2}}{dx} \\ $$ Commented by abdo mathsup 649 cc last updated on 29/Sep/19…
Question Number 135431 by 777316 last updated on 13/Mar/21 Answered by SEKRET last updated on 13/Mar/21 $$\boldsymbol{\mathrm{F}}\left(\boldsymbol{\mathrm{a}}\right)=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{ax}}^{\mathrm{2}} +\mathrm{1}\right)}{\left(\boldsymbol{\mathrm{x}}+\mathrm{1}\right)}\:\boldsymbol{\mathrm{dx}}\:\:\:\:\:\:\boldsymbol{\mathrm{a}}=\mathrm{1} \\ $$$$\boldsymbol{\mathrm{F}}\:'\left(\boldsymbol{\mathrm{a}}\right)=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\boldsymbol{\mathrm{x}}^{\mathrm{2}} }{\left(\boldsymbol{\mathrm{x}}+\mathrm{1}\right)\left(\boldsymbol{\mathrm{ax}}^{\mathrm{2}}…
Question Number 4297 by 123456 last updated on 07/Jan/16 $$\mathrm{lets} \\ $$$${f}:\left[\mathrm{0},+\infty\right)\rightarrow\mathbb{R},\forall{x}\geqslant{y}\Rightarrow{f}\left({x}\right)\geqslant{f}\left({y}\right) \\ $$$${g}:\left[\mathrm{0},+\infty\right)\rightarrow\mathbb{R} \\ $$$$\mathrm{if} \\ $$$$\forall{x}\in\left[\mathrm{0},+\infty\right),{f}\left({x}\right)\leqslant{g}\left({x}\right)\leqslant{f}\left(\mathrm{2}{x}\right) \\ $$$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}{f}\left({x}\right)=\mathrm{L},\mathrm{L}\:\mathrm{is}\:\mathrm{finite} \\ $$$$\mathrm{does} \\ $$$$\underset{{x}\rightarrow+\infty}…
Question Number 69829 by TawaTawa last updated on 28/Sep/19 Commented by TawaTawa last updated on 28/Sep/19 $$\mathrm{The}\:\mathrm{question}\:\mathrm{says}\:\mathrm{do}\:\mathrm{not}\:\mathrm{use}\:\mathrm{Newton}'\mathrm{s}\:\mathrm{law}\:\mathrm{and}\:\mathrm{kinematic} \\ $$ Commented by TawaTawa last updated on…
Question Number 135366 by Dwaipayan Shikari last updated on 12/Mar/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\:\sqrt[{\mathrm{6}}]{\mathrm{6}{x}−\mathrm{15}{x}^{\mathrm{2}} +\mathrm{20}{x}^{\mathrm{3}} −\mathrm{15}{x}^{\mathrm{4}} +\mathrm{6}{x}^{\mathrm{5}} −{x}^{\mathrm{6}} }}{dx}=\frac{\pi}{\mathrm{3}} \\ $$$${Or} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\:\sqrt[{{k}}]{{kx}−\frac{{k}\left({k}−\mathrm{1}\right)}{\mathrm{2}}{x}^{\mathrm{2}} +\frac{{k}\left({k}−\mathrm{1}\right)\left({k}−\mathrm{2}\right)}{\mathrm{6}}{x}^{\mathrm{3}}…
Question Number 4261 by 123456 last updated on 06/Jan/16 $${f}\left({x}\right){f}\left(\mathrm{1}−{x}\right)={f}\left(\mathrm{1}\right) \\ $$$${f}\left({x}\right)=? \\ $$ Commented by Yozzii last updated on 06/Jan/16 $${f}\left({x}\right)=\mathrm{0}\:{for}\:{example}.\: \\ $$$$ \\…
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Question Number 69778 by Rio Michael last updated on 27/Sep/19 $${prove}\:{that}\:{the}\:{equation}\: \\ $$$$\:\:\left({b}^{\mathrm{2}} −\mathrm{4}{ac}\right){x}^{\mathrm{2}} \:+\:\mathrm{4}\left({a}\:+\:{c}\right){x}\:−\mathrm{4}\:=\:\mathrm{0}\:{is}\:{always}\:{real}. \\ $$ Commented by prakash jain last updated on 28/Sep/19…
Question Number 69766 by Rio Michael last updated on 27/Sep/19 $${find}\:\:\frac{{dy}}{{dx}}\:\:{at}\:{the}\:{point}\:\:\left(\mathrm{0},\mathrm{3}\right)\:\:{when}\:\:\mathrm{2}{x}^{\mathrm{2}} {y}\:+\:{y}\:+\:\mathrm{4}{xy}^{\mathrm{2}} \:=\:\mathrm{2}{x}\:+\:\mathrm{3}\: \\ $$ Commented by kaivan.ahmadi last updated on 27/Sep/19 $${f}\left({x},{y}\right)=\mathrm{2}{x}^{\mathrm{2}} {y}+{y}+\mathrm{4}{xy}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{3}=\mathrm{0}…