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evaluate-sin-1-x-1-x-2-dx-




Question Number 8782 by uchechukwu okorie favour last updated on 27/Oct/16
evaluate; ∫((sin^(−1) x)/( (√(1−x^2 ))))dx
$${evaluate};\:\int\frac{\mathrm{sin}^{−\mathrm{1}} {x}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx} \\ $$
Answered by prakash jain last updated on 27/Oct/16
sin^(−1) x=u  (1/( (√(1−x^2 ))))dx=du  ∫((sin^(−1) x)/( (√(1−x^2 ))))dx=∫udu=(u^2 /2)+C=(((sin^(−1) x)^2 )/2)+C
$$\mathrm{sin}^{−\mathrm{1}} {x}={u} \\ $$$$\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx}={du} \\ $$$$\int\frac{\mathrm{sin}^{−\mathrm{1}} {x}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx}=\int{udu}=\frac{{u}^{\mathrm{2}} }{\mathrm{2}}+{C}=\frac{\left(\mathrm{sin}^{−\mathrm{1}} {x}\right)^{\mathrm{2}} }{\mathrm{2}}+{C} \\ $$

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