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Category: Integration

Question-149081

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}}…