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Category: Integration

2x-1-5x-2-x-2-dx-

Question Number 37028 by nishant last updated on 08/Jun/18 $$\int\frac{\mathrm{2}{x}−\mathrm{1}}{\mathrm{5}{x}^{\mathrm{2}} −{x}+\mathrm{2}}\:{dx}\:\:=\:\:? \\ $$ Answered by ajfour last updated on 08/Jun/18 $${I}=\frac{\mathrm{1}}{\mathrm{5}}\int\frac{\mathrm{10}{x}−\mathrm{1}}{\mathrm{5}{x}^{\mathrm{2}} −{x}+\mathrm{2}}{dx}\:−\frac{\mathrm{4}}{\mathrm{25}}\int\frac{{dx}}{\left({x}−\frac{\mathrm{1}}{\mathrm{10}}\right)^{\mathrm{2}} +\frac{\mathrm{2}}{\mathrm{5}}−\frac{\mathrm{1}}{\mathrm{100}}} \\ $$$$\:\:=\frac{\mathrm{1}}{\mathrm{5}}\mathrm{ln}\:\mid\mathrm{5}{x}^{\mathrm{2}}…

Question-37018

Question Number 37018 by behi83417@gmail.com last updated on 08/Jun/18 Commented by math khazana by abdo last updated on 08/Jun/18 $$\left.\mathrm{1}\right)\:{let}\:{I}\:=\:\int\:\:\:\frac{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{\mathrm{1}+{x}}{dx}\:{changement}\:{x}={sht}\:{give} \\ $$$${I}\:=\:\int\:\:\:\:\frac{{ch}\left({t}\right)}{\mathrm{1}+{sh}\left({t}\right)}{ch}\left({t}\right){dt}=\:\int\:\:\:\frac{{ch}^{\mathrm{2}} \left({t}\right){dt}}{\mathrm{1}+{sh}\left({t}\right)} \\…

Question-37004

Question Number 37004 by behi83417@gmail.com last updated on 07/Jun/18 Answered by tanmay.chaudhury50@gmail.com last updated on 07/Jun/18 $$\int\frac{\sqrt{\mathrm{1}+{x}^{{p}} \:\:}}{{x}}{dx} \\ $$$$\int\frac{\mathrm{1}+{x}^{{p}} }{{x}\sqrt{\mathrm{1}+{x}^{{p}} \:}}{dx} \\ $$$$\int\frac{{x}^{{p}−\mathrm{1}} \left(\mathrm{1}+{x}^{{p}}…

1-x-x-dx-

Question Number 36997 by rahul 19 last updated on 07/Jun/18 $$\int\:\sqrt{\frac{\mathrm{1}+{x}}{{x}}\:}{dx}\:=\:? \\ $$ Commented by behi83417@gmail.com last updated on 07/Jun/18 $${x}={tg}^{\mathrm{2}} {t}\Rightarrow{dx}=\mathrm{2}{tgt}\left(\mathrm{1}+{tg}^{\mathrm{2}} {t}\right){dt} \\ $$$${I}=\int\sqrt{\frac{\mathrm{1}+{tg}^{\mathrm{2}}…

Interval-in-which-given-function-is-decreasing-f-x-2-x-1-2-x-2-2-

Question Number 36957 by rahul 19 last updated on 07/Jun/18 $$\mathrm{Interval}\:\mathrm{in}\:\mathrm{which}\:\mathrm{given}\:\mathrm{function}\:\mathrm{is} \\ $$$${decreasing}. \\ $$$$\mathrm{f}\left({x}\right)=\:\left(\mathrm{2}^{{x}} −\mathrm{1}\right)\left(\mathrm{2}^{{x}} −\mathrm{2}\right)^{\mathrm{2}} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on…