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Question-137467




Question Number 137467 by SOMEDAVONG last updated on 03/Apr/21
Answered by Ñï= last updated on 03/Apr/21
I=∫(e^(−asin^(−1) x) /( (√(x^2 −1))))dx=∫(e^(−asin^(−1) x) /(i(√(1−x^2 ))))dx=(1/i)∫e^(−asin^(−1) x) d(sin^(−1) x)  =−(1/(ia))e^(−asin^(−1) x) +C=(i/a)e^(−asin^(−1) x) +C
$${I}=\int\frac{{e}^{−{a}\mathrm{sin}^{−\mathrm{1}} {x}} }{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{dx}=\int\frac{{e}^{−{a}\mathrm{sin}^{−\mathrm{1}} {x}} }{{i}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx}=\frac{\mathrm{1}}{{i}}\int{e}^{−{a}\mathrm{sin}^{−\mathrm{1}} {x}} {d}\left(\mathrm{sin}^{−\mathrm{1}} {x}\right) \\ $$$$=−\frac{\mathrm{1}}{{ia}}{e}^{−{a}\mathrm{sin}^{−\mathrm{1}} {x}} +{C}=\frac{{i}}{{a}}{e}^{−{a}\mathrm{sin}^{−\mathrm{1}} {x}} +{C} \\ $$

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