Evaluate: `int(cosecx)/(logtan(x/2))dx`

Explanation

Putting `log abs(tan frac{x}{2})=t`

`=>frac{frac{1}{2}sec^2 frac{x}{2}}{tan frac{x}{2}}dx=dt`

`=>frac{1}{2 sin frac{x}{2} cos frac{x}{2}}dx=dt`

`cosec xdx=dt`

`I=int frac{dt}{t}`

`=log (abs t)+C`

`I=log abs(log(tan frac{x}{2}))+C`