Solve it: ∫ tan x dx.

Concept Used:

tan(x) = sin(x) / cos(x).

Hence, the integral can be rewritten as:

∫ tan(x) dx = ∫ (sin(x) / cos(x)) dx.

We use substitution to simplify this expression.

Calculation:

Let cos(x) = u, then:

du = -sin(x) dx.

Substituting these into the integral:

∫ (sin(x) / cos(x)) dx = ∫ (-1 / u) du.

The integral of -1 / u is:

-ln |u| + C.

Substituting back u = cos(x):

-ln |cos(x)| + C.

∴ The solution to ∫ tan(x) dx is:

-ln(cos(x)) + C.

Hence, the correct answer is Option 2.