How to integrate cot(x)?

To integrate cot(x), use the substitution u = sin(x) and rewrite the integral as ∫(1/u)du.

To integrate cot(x), we can use the substitution u = sin(x). This gives us du/dx = cos(x), which means dx = du/cos(x). Substituting these into the integral, we get:

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

Now we can integrate using the natural logarithm:

∫(1/u)du = ln|u| + C
= ln|sin(x)| + C

Therefore, the final answer is:

∫cot(x)dx = ln|sin(x)| + C

It is important to note that this integral is undefined at x = nπ, where n is an integer, since cot(x) is undefined at these points.