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 $$=\int_{\mathrm{0}} ^{\:\Pi} \frac{\mathrm{dx}}{\mathrm{3}+\mathrm{2}×\frac{\mathrm{2tan}\frac{\mathrm{x}}{\mathrm{2}}}{\mathrm{1}+\mathrm{tan}^{\mathrm{2}}…
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Question Number 17033 by arnabpapu550@gmail.com last updated on 30/Jun/17 $$\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 $${I}=\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 17011 by arnabpapu550@gmail.com last updated on 29/Jun/17 $$\int_{\mathrm{0}} ^{\:\mathrm{a}} \mathrm{x}\sqrt{\frac{\mathrm{a}^{\mathrm{2}} −\mathrm{x}^{\mathrm{2}} }{\mathrm{a}^{\mathrm{2}} +\mathrm{x}^{\mathrm{2}} }}\mathrm{dx} \\ $$ Answered by sma3l2996 last updated on 29/Jun/17…
Question Number 17008 by arnabpapu550@gmail.com last updated on 29/Jun/17 $$\int_{\frac{\mathrm{1}\:}{\Pi}} ^{\frac{\mathrm{2}}{\Pi}} \:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\mathrm{sin}\frac{\mathrm{1}}{\mathrm{x}}\mathrm{dx} \\ $$ Answered by sma3l2996 last updated on 29/Jun/17 $${t}=\frac{\mathrm{1}}{{x}}\Rightarrow{dt}=\frac{−{dx}}{{x}^{\mathrm{2}} } \\…