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1-x-1-x-dx-




Question Number 20291 by tammi last updated on 25/Aug/17
(√(((1−x)/(1+x)) dx))
$$\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}\:{dx}} \\ $$
Answered by $@ty@m last updated on 25/Aug/17
=∫((1−x)/( (√(1−x^2 ))))dx  =∫(dx/( (√(1−x^2 ))))+(1/2)∫((−2x)/( (√(1−x^2 ))))dx  =sin^(−1) x+(√(1−x^2 ))+C
$$=\int\frac{\mathrm{1}−{x}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx} \\ $$$$=\int\frac{{dx}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}+\frac{\mathrm{1}}{\mathrm{2}}\int\frac{−\mathrm{2}{x}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx} \\ $$$$={sin}^{−\mathrm{1}} {x}+\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }+{C} \\ $$

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