Question

Integrate the given function w.r.t. respective variable : cot² x

Answer 1

Answer:

$\int cot^{2}\:x\:dx=-cot\:x-x+C$

Step-by-step explanation:

We know that before integrating any function ,we must convert it into integrable form.

As we know that

  $1+cot^{2}x=cosec^{2}x \\ \\ cot^{2}x=cosec^{2}x-1$

Now we can integrate it

$\int cot^{2}\:x\:dx\\ \\ \\ = \int\:cosec^{2}x-1\:dx\\ \\ \\ =\int\:cosec^{2}x\:dx-\int\:1\:dx\\\\=-cot\:x-x+C$