Question Number 82577 by M±th+et£s last updated on 22/Feb/20 $$\int\frac{\mathrm{2}−\sqrt{{x}+\mathrm{3}}}{\mathrm{2}+\sqrt{{x}−\mathrm{3}}}\:{dx} \\ $$ Commented by mathmax by abdo last updated on 22/Feb/20 $${let}\:{I}\:=\int\frac{\mathrm{2}−\sqrt{{x}+\mathrm{3}}}{\mathrm{2}+\sqrt{{x}+\mathrm{3}}}{dx}\:{vhangement}\:\mathrm{2}+\sqrt{{x}+\mathrm{3}}={t}\:{give} \\ $$$$\sqrt{{x}+\mathrm{3}}={t}−\mathrm{2}\:\Rightarrow{x}+\mathrm{3}\:=\left({t}−\mathrm{2}\right)^{\mathrm{2}} \:={t}^{\mathrm{2}}…
Question Number 82573 by Power last updated on 22/Feb/20 Commented by Tony Lin last updated on 22/Feb/20 $${let}\:{x}={asec}\theta,\:{dx}={asec}\theta{tan}\theta{d}\theta \\ $$$$\Rightarrow{sec}\theta=\frac{{x}}{{a}},\:{tan}\theta=\frac{\sqrt{{x}^{\mathrm{2}} −{a}^{\mathrm{2}} }}{{a}} \\ $$$${a}^{\mathrm{2}} \int{tan}^{\mathrm{2}}…
Question Number 17034 by arnabpapu550@gmail.com last updated on 30/Jun/17 $$\int_{\mathrm{0}} ^{\:\Pi} \frac{\mathrm{dx}}{\mathrm{3}+\mathrm{2sinx}+\mathrm{cosx}} \\ $$ Answered by Arnab Maiti last updated on 03/Jul/17 $$=\int_{\mathrm{0}} ^{\:\Pi} \frac{\mathrm{dx}}{\mathrm{3}+\mathrm{2}×\frac{\mathrm{2tan}\frac{\mathrm{x}}{\mathrm{2}}}{\mathrm{1}+\mathrm{tan}^{\mathrm{2}}…
Question Number 82571 by M±th+et£s last updated on 22/Feb/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 17033 by arnabpapu550@gmail.com last updated on 30/Jun/17 $$\int_{\frac{\Pi\:}{\mathrm{2}}} ^{\:\mathrm{0}} \:\frac{\mathrm{sinx}\:\mathrm{cosx}\:\mathrm{dx}}{\mathrm{2cos}^{\mathrm{2}} \mathrm{x}+\mathrm{3sin}^{\mathrm{2}} \mathrm{x}} \\ $$ Answered by sma3l2996 last updated on 30/Jun/17 $${t}={sinx}\Rightarrow{dt}={cosxdx} \\…
Question Number 82568 by jagoll last updated on 22/Feb/20 $$\int\:\frac{\mathrm{1}}{\mathrm{tan}\:{x}+\mathrm{cot}\:{x}+\mathrm{sec}\:{x}+\mathrm{cosec}\:{x}}\:{dx}\:? \\ $$ Answered by jagoll last updated on 22/Feb/20 Terms of Service Privacy Policy Contact:…
Question Number 17030 by tawa tawa last updated on 29/Jun/17 $$\int\:\mathrm{cot}^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{3}} \right)\:\mathrm{dx} \\ $$ Commented by Arnab Maiti last updated on 03/Jul/17 $$\mathrm{How}\:\mathrm{is}\:\mathrm{it}\:\mathrm{possible}\:?\:\int\mathrm{x}^{\mathrm{2}} \mathrm{cot}^{\mathrm{2}}…
Question Number 82566 by jagoll last updated on 22/Feb/20 $$\int\:\sqrt{\frac{{x}+\mathrm{1}}{{x}}}\:{dx}\:=\:? \\ $$ Commented by mathmax by abdo last updated on 22/Feb/20 $${let}\:{I}=\int\sqrt{\frac{{x}+\mathrm{1}}{{x}}}{dx}\:{changement}\:\sqrt{\frac{{x}+\mathrm{1}}{{x}}}={t}\:{give}\:\frac{{x}+\mathrm{1}}{{x}}={t}^{\mathrm{2}} \:\Rightarrow \\ $$$${x}+\mathrm{1}\:={xt}^{\mathrm{2}}…
Question Number 82560 by niroj last updated on 22/Feb/20 $$\:\boldsymbol{\mathrm{U}}\mathrm{se}\:\mathrm{gamma}\:\mathrm{function}\:\mathrm{to}\:\mathrm{prove} \\ $$$$\:\:\left(\mathrm{i}\right)\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \boldsymbol{\mathrm{sin}}^{\mathrm{4}} \boldsymbol{\mathrm{x}}\:\mathrm{2}\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{dx}}\:=\:\frac{\mathrm{3}\boldsymbol{\pi}−\mathrm{4}}{\mathrm{192}}. \\ $$$$\:\:\left(\mathrm{ii}\right)\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{6}}} \:\boldsymbol{\mathrm{cos}}^{\mathrm{4}} \mathrm{3}\boldsymbol{\theta}\:\mathrm{sin}^{\mathrm{2}} \mathrm{6}\theta\:=\:\frac{\mathrm{5}\pi}{\mathrm{192}}. \\ $$ Answered by…
Question Number 17010 by arnabpapu550@gmail.com last updated on 29/Jun/17 $$\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\mathrm{x}\left(\mathrm{tan}^{−\mathrm{1}} \mathrm{x}\right)^{\mathrm{2}} \mathrm{dx} \\ $$ Answered by sma3l2996 last updated on 29/Jun/17 $${I}=\int_{\mathrm{0}} ^{\mathrm{1}}…