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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Integrate : $\int e^x \bigg( \sin ^{-1} x +\large\frac{1}{\sqrt {1-x^2}}\bigg) dx $

$(a)\;e^x \sin ^{-1} x +c \\(b)\;\sin ^{-1}+c \\(c)\;x+c \\ (d)\;None$

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1 Answer

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$\int e^x \bigg( \sin ^{-1} x +\large\frac{1}{\sqrt {1-x^2}}\bigg) dx $
=> $ \int e^x . \sin ^{-1} x dx + e^x. \large\frac{1}{\sqrt {1-x^2}}$$dx$
=> $\sin ^{-1}x.e^x -\int \large\frac{1}{\sqrt {1+x^2}}$$ \times e^x dx \int e^x \times \large\frac{1}{\sqrt {1-x^2}}$$dx$
$e^x \sin ^{-1} x +c$
Hence a is the correct answer.
answered Dec 31, 2013 by meena.p
 

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