Question

` ∫   e^{m   sin ^-1  x}/ \sqrt{1-x^2}  ` dx

 

Answer 1

` ∫   e^{m   sin ^-1  x}/ \sqrt{1-x^2}  ` dx

 

\[\text{Let} \sin^{- 1} x = t\]
\[ \Rightarrow \frac{1}{\sqrt{1 - x^2}}dx = dt\]
Now,` ∫   e^{m   sin ^-1  x}/ \sqrt{1-x^2}  ` dx

\[ = \int e^\text{m t} \cdot dt\]
\[ = \frac{e^{mt}}{m} + C\]

` ∫   e^{m   sin ^-1  x}/m }  ` dx