$\displaystyle \int{\csc{x}\cot{x} \,}dx \,=\, -\csc{x}+c$
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.
$\displaystyle \int{\csc{x}\cot{x} \,}dx \,=\, -\csc{x}+c$
The integral of product of cosecant and cot functions formula can be written in terms of any variable in integral calculus.
$(1) \,\,\,$ $\displaystyle \int{\csc{(k)}\cot{(k)} \,}dk \,=\, -\csc{(k)}+c$
$(2) \,\,\,$ $\displaystyle \int{\csc{(m)}\cot{(m)} \,}dm \,=\, -\csc{(m)}+c$
$(3) \,\,\,$ $\displaystyle \int{\csc{(z)}\cot{(z)} \,}dz \,=\, -\csc{(z)}+c$
Learn how to derive the integration rule for the product of cosecant and cotangent functions in integral calculus.
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