The integral of cosec square x is equal to -cot(x)+C where C is a constant. In this post, we will learn how to integrate cosec^2x.

The integration formula of cosec^2x is given as follows:

∫cosec^{2}x dx = -cotx+C

## What is the Integration of cosec^2x

**Answer:** The integration of cosec^{2}x is -cotx+C.

*Proof:*

First, recall the function whose derivative is the function cosec^{2}x. We know that the derivative of cotx is equal to -cosec^{2}x, and so we have that

$\dfrac{d}{dx}$(-cot x) = cosec^{2}x.

Now, we integrate both sides. As a result, we get that

∫$\dfrac{d}{dx}$(-cot x) = ∫cosec^{2}x dx +c, c is an integral constant.

⇒ -cotx = ∫cosec^{2}x dx +c, by the fact: integration is the opposite process of derivatives.

⇒ ∫cosec^{2}x dx = -cotx -c

⇒ ∫cosec^{2}x dx = -cotx +C where C= -c.

So the integration of cosec^{2}x (cosec square x) is equal to -cotx+C where C denotes an integral constant.

**Read These Derivatives:**

## FAQs

**Q1: What is the integration of cosec square x?**

Answer: The integration of cosec square x is equal to ∫cosec^{2}x dx = -cotx +C where C is a constant.