trigonometric function: $\displaystyle \int \dfrac{dx}{\cos(x) \sin(x)}$

$\displaystyle \int \dfrac{dx}{\cos x \, \sin x} = 2\int \dfrac{dx}{2\cos x \, \sin x}$

      $= 2\displaystyle \int \dfrac{dx}{\sin 2x}$

      $= 2\displaystyle \int \csc 2x \, dx$

      $= \displaystyle \int \csc 2x \, (2 \, dx)$

      $= \ln (\csc 2x - \cot 2x) + C$           answer