Evaluate the integral of cos(x) dx.

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

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

∫cos(x) dx = ∫cos(x) (du/cos(x))
= ∫du
= u + C
= sin(x) + C

Therefore, the integral of cos(x) dx is sin(x) + C, where C is the constant of integration. This result can also be verified by differentiating sin(x) + C with respect to x, which gives cos(x) as required.