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प्रश्न
\[\int\frac{\left\{ e^{\sin^{- 1} }x \right\}^2}{\sqrt{1 - x^2}} dx\]
उत्तर
\[\int\frac{\left( e^\{sin^{- 1} x \right)^2}{\sqrt{1 - x^2}} dx\]
` Let e^{sin-1 _x }= t `
Differentiating both sides w . r . t . x,
`e^{sin-1 _x } × 1 / \sqrt{ 1 - x^2 } ` dx = dt
` Now , ∫ (e^{sin-1 _ x }) ^2/ \sqrt{1-x^2} ` dx
` ∫ e^{sin-1 _x } . {e^{sin-1 _ x }}/ \sqrt{1-x^2} ` dx
` ∫ t . dt
\[ = \frac{t^2}{2} + C\]
` (e^{sin-1 _x })^2 /2 + C`
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