# Integral & Antiderivative of cotx: Formula, Proof

The antiderivative of cotx is ln|sinx|+C where ln denotes the logarithm with base e and C is a constant. In this post, we will learn how to find the antiderivative of cotx.

The integral of cotx or the antiderivative formula of cotx is given by

∫cotx dx = ln|sinx| + C,

where C is an integration constant.

## Find the Antiderivative of cotx

We know that if the antiderivative of cotx is a function f(x), then the derivative of f(x) becomes cotx. So the antiderivative of cotx will be the integration of cotx, that is, we need to find the integral

∫ cotx dx.

Put ln sinx = z

Differentiating both sides, we get that

$\dfrac{1}{\sin x}$ cosx dx = dz

⇒ cotx dx = dz

Thus the integral of cot x will be

∫ cotx dx

= ∫ dz

= z + C

= ln sinx + C

As logarithms are defined for positive values, we obtain that

∫cotx dx = ln|sinx|+C.

So the antiderivative of cotx is ln|sinx|+C where C is a constant on integration.

Verification:

Let’s verify that the derivative of ln|sinx|+C is the function cotx. Now, the derivative of ln|sinx|+C equals

d/dx(ln|sinx|+C)

= cotx + 0 as the derivative of a constant is zero.

= cotx, hence verified.

Antiderivative of 1

Antiderivative of x

Antiderivative of 1/x

Antiderivative of ln x

Antiderivative of tan x

## FAQs

### Q1: What is antiderivative of cotx?

Answer: The antiderivative of cot x is equal to ln|sinx|+C where C is an integral constant.