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Category: Algebra

1-x-ln-x-x-2-1-dx-

Question Number 148887 by mathdanisur last updated on 01/Aug/21 $$\Omega=\underset{\:\mathrm{1}} {\overset{\:\infty} {\int}}\:\frac{\sqrt{{x}}\:{ln}\:{x}}{{x}^{\mathrm{2}} \:+\:\mathrm{1}}\:{dx}\:=\:? \\ $$ Answered by Kamel last updated on 01/Aug/21 $$\Omega=\underset{\:\mathrm{1}} {\overset{\:\infty} {\int}}\:\frac{\sqrt{{x}}\:{ln}\:{x}}{{x}^{\mathrm{2}}…

Find-the-maximum-and-minimum-of-the-expression-i-1-n-a-i-x-i-with-i-1-n-x-i-b-i-2-c-2-where-a-i-b-i-and-c-are-constants-extracted-and-modified-from-Q83331-

Question Number 83341 by mr W last updated on 01/Mar/20 $${Find}\:{the}\:{maximum}\:{and}\:{minimum} \\ $$$${of}\:{the}\:{expression}\:\underset{\boldsymbol{{i}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\boldsymbol{\sum}}{a}}_{\boldsymbol{{i}}} \boldsymbol{{x}}_{\boldsymbol{{i}}} \:{with} \\ $$$$\underset{\boldsymbol{{i}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\boldsymbol{\sum}}}\left(\boldsymbol{{x}}_{\boldsymbol{{i}}} −\boldsymbol{{b}}_{\boldsymbol{{i}}} \right)^{\mathrm{2}} =\boldsymbol{{c}}^{\mathrm{2}} ,\:{where}\:\boldsymbol{{a}}_{\boldsymbol{{i}}}…

Question-148861

Question Number 148861 by mathdanisur last updated on 31/Jul/21 Answered by dumitrel last updated on 01/Aug/21 $$\left(\mathrm{2}{x}\right)^{\mathrm{4}} +\mathrm{324}=\left(\mathrm{4}{x}^{\mathrm{2}} −\mathrm{12}{x}+\mathrm{18}\right)\left(\mathrm{4}{x}^{\mathrm{2}} +\mathrm{12}{x}+\mathrm{18}\right) \\ $$$${f}\left({x}\right)=\mathrm{4}{x}^{\mathrm{2}} −\mathrm{12}{x}+\mathrm{18}\Rightarrow{f}\left({x}+\mathrm{3}\right)=\mathrm{4}{x}^{\mathrm{2}} +\mathrm{12}{x}+\mathrm{18} \\…

1-2-3-4-1-3-4-5-1-4-5-6-1-5-6-7-1-6-7-8-1-12-13-14-

Question Number 148838 by liberty last updated on 31/Jul/21 $$\:\frac{\mathrm{1}}{\mathrm{2}×\mathrm{3}×\mathrm{4}}\:+\frac{\mathrm{1}}{\mathrm{3}×\mathrm{4}×\mathrm{5}}+\frac{\mathrm{1}}{\mathrm{4}×\mathrm{5}×\mathrm{6}}+\frac{\mathrm{1}}{\mathrm{5}×\mathrm{6}×\mathrm{7}}+\frac{\mathrm{1}}{\mathrm{6}×\mathrm{7}×\mathrm{8}}+…+\frac{\mathrm{1}}{\mathrm{12}×\mathrm{13}×\mathrm{14}}=? \\ $$ Commented by JDamian last updated on 31/Jul/21 $${Can}\:{you}\:{confirm}\:{there}\:{is}\:{a}\:{missing}\:\frac{\mathrm{1}}{\mathrm{4}×\mathrm{5}×\mathrm{6}}? \\ $$ Commented by liberty…