Integral of ctgxcscx dx

1. The integral of a constant times a function is the constant times the integral of the function:

   $$\int \cot{\left(x \right)} \csc{\left(x \right)}\, dx = - \int \left(- \cot{\left(x \right)} \csc{\left(x \right)}\right)\, dx$$

   1. The integral of cosecant times cotangent is cosecant:

      $$\int \left(- \cot{\left(x \right)} \csc{\left(x \right)}\right)\, dx = \csc{\left(x \right)}$$

   So, the result is: $- \csc{\left(x \right)}$

2. Add the constant of integration:

   $$- \csc{\left(x \right)}+ \mathrm{constant}$$

The answer is:

$$- \csc{\left(x \right)}+ \mathrm{constant}$$