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.
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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.