# Integration of cotx: Formula, Proof | cotx Integration

The integration of cotx is ln|sinx|, where ln denotes the natural logarithm, that is, the logarithm with base e. Here we will learn how to find the integral of cotx dx.

## cotx Integration Formula

The cotx integration formula is given below.

∫cotx dx = ln|sinx|+C

## Integration of cotx Proof

We will show that ∫cotx dx = ln|sinx|+C. As $\cot x =\dfrac{\cos x}{\sin x}$, the integral of cotx will be equal to

∫cotx dx = $\int \dfrac{\cos x}{\sin x} \ dx$ …(*)

In the above integral, let us put sinx=t.

Differentiating both sides, cosx dx = dt.

So we have from (*) that

∫cotx dx = $\int \dfrac{dt}{t}$

= ln|t|+C where C is a constant of integration

= ln|sinx|+C as t=sinx.

So the integration of cotx is equal to ln|sinx|+C which is proved by the substitution method of integrations.

Video Solution on Integration of cotx:

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Integration cube root of x

Integration of 1/√x

Derivative of √x

## FAQs

Q1: What is the Integration of cotx?

Answer: The integration of cotx is ln|sinx|+C where C is the integration constants.