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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