Integral of e^xsin(y)dx dx

1. The integral of a constant times a function is the constant times the integral of the function:

   $$\int e^{x} \sin{\left(y \right)}\, dx = \sin{\left(y \right)} \int e^{x}\, dx$$

   1. The integral of the exponential function is itself.

      $$\int e^{x}\, dx = e^{x}$$

   So, the result is: $e^{x} \sin{\left(y \right)}$

2. Add the constant of integration:

   $$e^{x} \sin{\left(y \right)}+ \mathrm{constant}$$

The answer is:

$$e^{x} \sin{\left(y \right)}+ \mathrm{constant}$$