Evaluate: `int1/(sinx(2+3cosx)\ dx`

Explanation

`sinx=frac{2tanx/2}{1+tan^2x/2}`

`cosx=frac{1-tan^x/2}{1+tan^x/2}`

`=int frac{sec^2x/2}{2tanx/2(2+2tan^2x/2+3-3tan^2 x/2)}dx`

`tanx/2=t=>1/.sec^2 x/2dx=dt`

`=int frac{t^(-3)}{5t^2-1}dt`

`t^(-2)=k=>-2.t^(-3)dt=dk`

`=-1/10 int frac{dk}{k}`

`=1/10(5/(t^2)-1)^2`
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