Question Number 82614 by jagoll last updated on 23/Feb/20 $$\int\:\frac{\mathrm{sin}\:\mathrm{2}{x}}{\mathrm{sin}\:\mathrm{5}{x}\:\mathrm{sin}\:\mathrm{3}{x}}\:{dx}\:?\: \\ $$ Answered by jagoll last updated on 23/Feb/20 Terms of Service Privacy Policy Contact:…
Question Number 82604 by jagoll last updated on 23/Feb/20 $$\int\:\frac{\mathrm{cos}\:\left(\mathrm{5}{x}\right)+\mathrm{cos}\:\left(\mathrm{4}{x}\right)\:{dx}}{\mathrm{1}−\mathrm{2cos}\:\left(\mathrm{3}{x}\right)}\:=\: \\ $$ Answered by john santu last updated on 23/Feb/20 $$\int\:\:\frac{\left\{\mathrm{cos}\:\left(\mathrm{5}{x}\right)+\mathrm{cos}\:\left(\mathrm{4}{x}\right)\right\}\mathrm{sin}\:\left(\mathrm{3}{x}\right)}{\mathrm{sin}\:\left(\mathrm{3}{x}\right)−\mathrm{sin}\:\left(\mathrm{6}{x}\right)}\:{dx} \\ $$$$=\mathrm{2}\int\:\frac{\left\{\mathrm{cos}\:\left(\frac{\mathrm{9}{x}}{\mathrm{2}}\right)\mathrm{cos}\:\left(\frac{{x}}{\mathrm{2}}\right)\right\}\mathrm{sin}\:\left(\mathrm{3}{x}\right)}{\mathrm{2cos}\:\left(\frac{\mathrm{9}{x}}{\mathrm{2}}\right)\mathrm{sin}\:\left(−\frac{\mathrm{3}{x}}{\mathrm{2}}\right)}\:{dx} \\ $$$$=\:−\:\int\:\frac{\mathrm{sin}\:\left(\mathrm{3}{x}\right)\mathrm{cos}\:\left(\frac{{x}}{\mathrm{2}}\right)}{\mathrm{sin}\:\left(\frac{\mathrm{3}{x}}{\mathrm{2}}\right)}\:{dx}\:…
Question Number 148128 by puissant last updated on 25/Jul/21 $$\int\mathrm{ln}\left(\mathrm{sin}\left(\mathrm{x}\right)\right)\mathrm{dx} \\ $$ Answered by Olaf_Thorendsen last updated on 25/Jul/21 $$\mathrm{Pas}\:\mathrm{de}\:\mathrm{formule}\:\mathrm{explicite}\:\mathrm{pour}\:\mathrm{ce}\:\mathrm{genre} \\ $$$$\mathrm{d}'\mathrm{integrales}\:\mathrm{mais}\:\mathrm{on}\:\mathrm{peut}\:\mathrm{quand}\:\mathrm{meme} \\ $$$$\mathrm{calculer}\:\mathrm{la}\:\mathrm{valeur}\:\mathrm{sur}\:\mathrm{un}\:\mathrm{intervalle}\:\mathrm{bien} \\…
Question Number 82577 by M±th+et£s last updated on 22/Feb/20 $$\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}}…
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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}}…