How to Integrate 1 + sin(x)?

To integrate the function 1 + sin(x), we will break it down into two separate parts:

1. The integral of 1
2. The integral of sin(x)

First, let’s integrate 1:

∫ 1 \, dx = x

Next, we integrate sin(x):

∫ sin(x) \, dx = -cos(x)

Now, we can combine both results:

∫ (1 + sin(x)) \, dx = x – cos(x) + C

Here, C is the constant of integration. So, the final answer is:

∫ (1 + sin(x)) \, dx = x – cos(x) + C