Find the indefinite integral. (Remember the constant of integration.) \[ \int 4^{\sin (x)} \cos (x) d x \]

Step 1 ：Let \( u = \sin(x) \), then \( du = \cos(x) dx \)

Step 2 ：Substitute \( u \) into the integral, the integral becomes \( \int 4^u du \)

Step 3 ：Solve the integral directly to get \( \frac{4^u}{\ln(4)} \)

Step 4 ：Substitute \( \sin(x) \) back for \( u \) to get \( \frac{4^{\sin(x)}}{\ln(4)} \)

Step 5 ：Simplify the final answer to get \( \frac{4^{\sin(x)}}{2\ln(2)} \)

Step 6 ：\(\boxed{\text{Final Answer: The indefinite integral of } 4^{\sin (x)} \cos (x) \text{ with respect to } x \text{ is } \frac{4^{\sin(x)}}{2\ln(2)} + C, \text{ where } C \text{ is the constant of integration.}}\)