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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Integrate : $\int \large \frac{e^{\Large a \sin ^{-1} x}}{\sqrt {1-x^2}}$$.dx$

\[\begin {array} {1 1} (a)\;e^{a \cos^{-1}(x)}+c \\ (b)\;e^{ \sin ^{-1} (x)}+c \\ (c)\;\frac{e^{a \sin ^{-1} (x)}}{a}+c \\ (d)\;None \end {array}\]

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1 Answer

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$\sin t x =t$
=> $\large\frac{1}{\sqrt {1-x^2}}$$dx=dt$
=> $\int e^{at}.dt$
=> $\large\frac{e^{at}}{a} $$+c$
=> $\large\frac{e^{a \sin ^{-1}x }}{a}+c$
Hence c is the correct answer.
answered Dec 19, 2013 by meena.p
 
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