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Category: Integration

dx-x-x-2-2x-1-tan-1-x-1-x-2-2x-1-C-I-m-confused-in-choosing-the-right-substitution-so-that-we-can-get-the-result-above-Please-help-

Question Number 46369 by Joel578 last updated on 24/Oct/18 $$\int\:\frac{{dx}}{{x}\sqrt{{x}^{\mathrm{2}} \:+\:\mathrm{2}{x}\:−\:\mathrm{1}}}\:\:=\:\mathrm{tan}^{−\mathrm{1}} \left(\frac{{x}\:−\:\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} \:+\:\mathrm{2}{x}\:−\:\mathrm{1}}}\right)\:+\:{C} \\ $$$$ \\ $$$$\mathrm{I}'\mathrm{m}\:\mathrm{confused}\:\mathrm{in}\:\mathrm{choosing}\:\mathrm{the}\:\mathrm{right}\:\mathrm{substitution} \\ $$$$\mathrm{so}\:\mathrm{that}\:\mathrm{we}\:\mathrm{can}\:\mathrm{get}\:\mathrm{the}\:\mathrm{result}\:\mathrm{above}. \\ $$$$\mathrm{Please}\:\mathrm{help}… \\ $$ Commented by…

bemath-2-cos-x-2-cos-x-dx-

Question Number 111873 by bemath last updated on 05/Sep/20 $$\:\:\:\sqrt{{bemath}} \\ $$$$\int\:\frac{\mathrm{2}−\mathrm{cos}\:{x}}{\mathrm{2}+\mathrm{cos}\:{x}}\:{dx}\: \\ $$ Answered by Lordose last updated on 05/Sep/20 $$ \\ $$$$\boldsymbol{\mathrm{Set}}\:\boldsymbol{\mathrm{u}}=\boldsymbol{\mathrm{tan}}\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\:\Rightarrow\boldsymbol{\mathrm{du}}=\frac{\mathrm{1}}{\mathrm{2}}\boldsymbol{\mathrm{sec}}^{\mathrm{2}} \frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\boldsymbol{\mathrm{dx}}…

1a-dx-e-5x-e-3x-e-2x-1b-dx-e-5x-e-3x-e-2x-2a-dx-x-5-3-x-3-5-2b-dx-x-5-3-x-3-5-

Question Number 46323 by MJS last updated on 24/Oct/18 $$\left(\mathrm{1}{a}\right)\:\:\int\frac{{dx}}{\mathrm{e}^{\mathrm{5}{x}} +\mathrm{e}^{\mathrm{3}{x}} +\mathrm{e}^{\mathrm{2}{x}} }=? \\ $$$$\left(\mathrm{1}{b}\right)\:\:\int\frac{{dx}}{\mathrm{e}^{\mathrm{5}{x}} −\mathrm{e}^{\mathrm{3}{x}} −\mathrm{e}^{\mathrm{2}{x}} }=? \\ $$$$\left(\mathrm{2}{a}\right)\:\:\int\frac{{dx}}{{x}^{\frac{\mathrm{5}}{\mathrm{3}}} +{x}^{\frac{\mathrm{3}}{\mathrm{5}}} }=? \\ $$$$\left(\mathrm{2}{b}\right)\:\:\int\frac{{dx}}{{x}^{\frac{\mathrm{5}}{\mathrm{3}}} −{x}^{\frac{\mathrm{3}}{\mathrm{5}}}…

bemath-1-cos-x-2-cos-x-dx-2-f-x-x-3-f-x-

Question Number 111818 by bemath last updated on 05/Sep/20 $$\:\:\:\sqrt{{bemath}\:} \\ $$$$\left(\mathrm{1}\right)\int\:\frac{\mathrm{cos}\:{x}}{\mathrm{2}−\mathrm{cos}\:{x}}\:{dx}\: \\ $$$$\left(\mathrm{2}\right)\:{f}\left({x}\right)\:=\:\mid{x}^{\mathrm{3}} \mid\:\Rightarrow\:{f}\:'\left({x}\right)\:? \\ $$ Answered by bobhans last updated on 05/Sep/20 $$\mathrm{f}\left(\mathrm{x}\right)\:=\:\mid\mathrm{x}^{\mathrm{3}}…

Question-46252

Question Number 46252 by rahul 19 last updated on 23/Oct/18 Answered by MJS last updated on 23/Oct/18 $${r}=\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }=\sqrt{\left(\mathrm{cos}^{\mathrm{2}} \:\theta\:+\mathrm{sin}^{\mathrm{2}} \:\theta\right)\mathrm{cos}^{\mathrm{2}} \:\mathrm{4}\theta}=\mid\mathrm{cos}\:\mathrm{4}\theta\mid \\ $$$$\left.\Rightarrow\:{A}\right)…