Question Number 83603 by jagoll last updated on 04/Mar/20 $$\int\:\frac{\mathrm{dx}}{\mathrm{1}−\mathrm{2cos}\:\mathrm{x}} \\ $$ Commented by turbo msup by abdo last updated on 04/Mar/20 $${we}\:{use}\:{the}\:{changement}\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t} \\ $$$$\Rightarrow\int\:\:\frac{{dx}}{\mathrm{1}−\mathrm{2}{cosx}}\:=\int\:\:\frac{\mathrm{1}}{\mathrm{1}−\mathrm{2}\frac{\mathrm{1}−{t}^{\mathrm{2}}…
Question Number 83597 by dennis kenneth last updated on 04/Mar/20 $$\int_{\mathrm{0}} ^{\mathrm{2}} \left(\mathrm{3}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{2}\right){dx} \\ $$ Commented by Jidda28 last updated on 04/Mar/20 $$\left.=\:\:{x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}}…
Question Number 149113 by bramlexs22 last updated on 03/Aug/21 $$\:\int_{\mathrm{0}} ^{\:\pi} \:\frac{\mathrm{cos}\:^{\mathrm{3}} \mathrm{x}}{\mathrm{7}−\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}}\:\mathrm{dx}\:=? \\ $$ Answered by mathmax by abdo last updated on 03/Aug/21…
Question Number 149112 by bramlexs22 last updated on 03/Aug/21 $$\:\varphi\:=\:\int\:\mathrm{tan}\:\left(\mathrm{x}+\frac{\pi}{\mathrm{3}}\right)\mathrm{tan}\:\mathrm{3x}\:\mathrm{tan}\:\left(\mathrm{2x}−\frac{\pi}{\mathrm{3}}\right)\:\mathrm{dx}\:=? \\ $$ Commented by som(math1967) last updated on 03/Aug/21 $$\boldsymbol{{tan}}\mathrm{3}\boldsymbol{{x}}=\boldsymbol{{tan}}\left(\boldsymbol{{x}}+\frac{\boldsymbol{\pi}}{\mathrm{3}}\:+\mathrm{2}\boldsymbol{{x}}−\frac{\boldsymbol{\pi}}{\mathrm{3}}\right) \\ $$$$\boldsymbol{{tan}}\mathrm{3}\boldsymbol{{x}}=\frac{\boldsymbol{{tan}}\left(\boldsymbol{{x}}+\frac{\boldsymbol{\pi}}{\mathrm{3}}\right)+\boldsymbol{{tan}}\left(\mathrm{2}\boldsymbol{{x}}−\frac{\boldsymbol{\pi}}{\mathrm{3}}\right)}{\mathrm{1}−{tan}\left(\boldsymbol{{x}}+\frac{\boldsymbol{\pi}}{\mathrm{3}}\right)\boldsymbol{{tan}}\left(\mathrm{2}\boldsymbol{{x}}+\frac{\mathrm{2}\boldsymbol{\pi}}{\mathrm{3}}\right)} \\ $$$$\therefore\boldsymbol{{tan}}\mathrm{3}\boldsymbol{{xtan}}\left(\boldsymbol{{x}}+\frac{\boldsymbol{\pi}}{\mathrm{3}}\right)\boldsymbol{{tan}}\left(\mathrm{2}\boldsymbol{{x}}−\frac{\boldsymbol{\pi}}{\mathrm{3}}\right) \\…
Question Number 83569 by mathmax by abdo last updated on 03/Mar/20 $${calculate}\:\int_{\mathrm{1}} ^{+\infty} \:\frac{{dx}}{{x}^{\mathrm{4}} \left(\mathrm{3}{x}−\mathrm{1}\right)^{\mathrm{5}} } \\ $$ Commented by mathmax by abdo last updated…
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Question Number 18024 by mondodotto@gmail.com last updated on 13/Jul/17 Answered by sma3l2996 last updated on 14/Jul/17 $${I}=\int\frac{\mathrm{5}{x}+\mathrm{3}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{10}}}{dx}=\frac{\mathrm{5}}{\mathrm{2}}\int\frac{\mathrm{2}{x}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{10}}}{dx}+\int\frac{\mathrm{3}{dx}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{10}}} \\ $$$$=\frac{\mathrm{5}}{\mathrm{2}}\int\frac{\mathrm{2}{x}+\mathrm{4}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{10}}}+\int\frac{\mathrm{3}−\mathrm{10}}{\:\sqrt{\left({x}+\mathrm{2}\right)^{\mathrm{2}} +\mathrm{6}}}{dx} \\…
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Question Number 149081 by Integrals last updated on 02/Aug/21 Answered by Ar Brandon last updated on 02/Aug/21 $$\phi=\int\frac{{d}\beta}{\mathrm{2}−\mathrm{3sin}\beta}\:,\:{t}=\mathrm{tan}\frac{\beta}{\mathrm{2}} \\ $$$$\:\:\:=\int\frac{\mathrm{2}}{\mathrm{2}−\mathrm{3}\left(\frac{\mathrm{2}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }\right)}\centerdot\frac{{dt}}{\mathrm{1}+{t}^{\mathrm{2}} }=\int\frac{{dt}}{{t}^{\mathrm{2}} −\mathrm{3}{t}+\mathrm{1}} \\ $$$$\:\:\:=\int\frac{{dt}}{\left({t}−\frac{\mathrm{3}}{\mathrm{2}}\right)^{\mathrm{2}}…
Question Number 83521 by M±th+et£s last updated on 03/Mar/20 $$\int\frac{\sqrt{{sin}\left({x}\right)}}{{sin}^{\mathrm{2}} \left({x}\right)+\mathrm{1}}\:{dx} \\ $$ Commented by msup trace by abdo last updated on 04/Mar/20 $${changement}\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}\:{give} \\…