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

Question

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