∫ cot x · dx =

To find the integral of cot x, we can use a known identity and some basic integration techniques. The cotangent function can be expressed as the ratio of cosine and sine:

Integral of Cotangent

The integral of cot x can be rewritten as:

∫ cot x · dx = ∫ (cos x / sin x) · dx

Using Substitution

To solve this integral, we can use the substitution method. Let:

• u = sin x
• du = cos x · dx

Now, we can rewrite the integral in terms of u:

∫ (1/u) · du

Final Steps

The integral of 1/u is:

ln |u| + C

Substituting back for u gives us:

ln |sin x| + C

Result

Thus, the integral of cot x is:

∫ cot x · dx = ln |sin x| + C