Math Doubts

Integral of cscx.cotx formula


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


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.

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

Alternative forms

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

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

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

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


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

Math Doubts
Math Doubts is a free math tutor for helping students to learn mathematics online from basics to advanced scientific level for teachers to improve their teaching skill and for researchers to share their research projects. Know more
Follow us on Social Media
Math Problems

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.

Learn more