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Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Q)

Integrate : $\int a ^{\log ax}. \sin b dx $

\[\begin {array} {1 1} (a)\;a^{\log ax}. \log a \sin b +c \\ (b)\;a. \log a \cos b +c \\ (c)\;\frac{x^2}{2} \sin b+c \\ (d)\;None \end {array}\]

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A)
$\int a ^{\log ax}. \sin b dx$
By using properties:
$a^{\log ax}=x$
$\int x. \sin b dx $
=> $ \sin b . \large\frac{x^2}{2}$$+c$
Hence c is the correct answer.
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