`int e^(cotx) (cos x - cosec x ) dx` is equal to :

Explanation

`int e^(cotx) (cosx-cosecx) dx`

Let `y = e^(cotx)sinx`

`:. dy/dx = e^cotx cosx +sinx e^cotx(-cosec^2x)`

`=> dy/dx = e^cotx cosx - sinx e^cotx(cosec x)`

`=> dy/dx = e^cotx(cos-cosecx)`

Now, integrating both sides,

`y+c = int e^(cotx) (cosx-cosecx) dx`

`=> int e^(cotx) (cosx-cosecx) dx = e^(cotx)sinx+c`

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