Evaluate the integral of sin(x) dx.

The integral of sin(x) dx is -cos(x) + C, where C is the constant of integration.

To evaluate the integral of sin(x) dx, we can use integration by substitution. Let u = cos(x), then du/dx = -sin(x) and dx = du/-sin(x). Substituting these into the integral, we get:

∫sin(x) dx = ∫sin(x) (-sin(x)/-sin(x)) dx
= -∫sin(x)/cos(x) d(cos(x))
= -∫tan(x) d(cos(x))

Using the formula for the integral of tan(x), we get:

= -ln|cos(x)| + C

Since u = cos(x), we can substitute back to get:

= -ln|u| + C
= -ln|cos(x)| + C

Therefore, the integral of sin(x) dx is -cos(x) + C.