# Integral of cscx.cotx formula

## Formula

$\displaystyle \int{\csc{x}\cot{x} \,}dx \,=\, -\csc{x}+c$

### Introduction

Assume, $x$ as a variable, and represents an angle of a right triangle. The cosecant and cotangent functions are written in terms of $x$ as $\csc{x}$ or $\operatorname{cosec}{x}$ and $\cot{x}$ respectively. The indefinite integral of product of $\csc{x}$ and $\cot{x}$ functions with respect to $x$ is written in the following mathematical form in integral calculus.

$\displaystyle \int{\csc{x}\cot{x} \,} dx$

The indefinite integration of product of cosecant and cot functions with respect to $x$ is equal to the sum of negative cosecant function and an integral constant.

$\displaystyle \int{\csc{x}\cot{x} \,}dx \,=\, -\csc{x}+c$

#### Alternative forms

The integral of product of cosecant and cot functions formula can be written in terms of any variable in integral calculus.

$(1) \,\,\,$ $\displaystyle \int{\csc{(k)}\cot{(k)} \,}dk \,=\, -\csc{(k)}+c$

$(2) \,\,\,$ $\displaystyle \int{\csc{(m)}\cot{(m)} \,}dm \,=\, -\csc{(m)}+c$

$(3) \,\,\,$ $\displaystyle \int{\csc{(z)}\cot{(z)} \,}dz \,=\, -\csc{(z)}+c$

### Proof

Learn how to derive the integration rule for the product of cosecant and cotangent functions in integral calculus.

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Jun 26, 2023

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