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Category: Integration

tan-arc-sin-x-dx-

Question Number 91004 by jagoll last updated on 27/Apr/20 $$\int\:\mathrm{tan}\:\left({arc}\:\mathrm{sin}\:{x}\right)\:{dx} \\ $$ Commented by jagoll last updated on 27/Apr/20 $${let}\:\mathrm{sin}^{−\mathrm{1}} \left({x}\right)\:=\:{y}\:\Rightarrow{x}\:=\:\mathrm{sin}\:{y} \\ $$$${dx}\:=\:\mathrm{cos}\:{y}\:{dy}\: \\ $$$$\mathrm{tan}\:\left(\mathrm{sin}^{−\mathrm{1}}…

dx-3tan-x-cos-x-

Question Number 156517 by cortano last updated on 12/Oct/21 $$\int\:\frac{\mathrm{dx}}{\mathrm{3tan}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}}\:=? \\ $$ Answered by puissant last updated on 12/Oct/21 $${Q}=\int\frac{{dx}}{\mathrm{3}{tanx}+{cosx}} \\ $$$$=\int\frac{{cosx}}{{cos}^{\mathrm{2}} {x}+\mathrm{3}{sinx}}{dx}\:=\:\int\frac{{cosx}}{\mathrm{1}−{sin}^{\mathrm{2}} +\mathrm{3}{sinx}}{dx} \\…