Integral of exp^(x+y)dx dx

1. There are multiple ways to do this integral.

   Method #1

   1. Let $u = x + y$.

      Then let $du = dx$ and substitute $du$:

      $$\int e^{u}\, du$$

      1. The integral of the exponential function is itself.

         $$\int e^{u}\, du = e^{u}$$

      Now substitute $u$ back in:

      $$e^{x + y}$$

   Method #2

   1. Rewrite the integrand:

      $$e^{x + y} = e^{x} e^{y}$$

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

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

      1. The integral of the exponential function is itself.

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

      So, the result is: $e^{x} e^{y}$

2. Add the constant of integration:

   $$e^{x + y}+ \mathrm{constant}$$

The answer is:

$$e^{x + y}+ \mathrm{constant}$$