Evaluate : `int e^(x) [(cos x - sin x)/(sin^(2) x)] dx.`

Explanation

We have,
`int e^(x) *[(cos x - sin x)/(sin^(2)x)] * dx`
` = int e^(x) [1/(sin x) * (cos x)/(sin x) - (sin x)/(sin ^(2) x)]* dx`
` = f e^(x) [cosec" " x * cot" " x - cosec " "x] * dx `
` = f e^(x) * cosec " "x* cot" " x " "dx- f e^(x) cosec " " x" " dx `
`=int e^(x) cosec" " x * cot " " x " " dx-`
`[cosec " "x int e^(x) dx - int (d/(dx) (cosec" " x)int e^(x)" "dx)dx]`
` = int e^(x) [cosec" "x * cot " " x" " dx-[e^(x) cosec" " x+ int e^(x) cosec" " x * cot " " x " " dx]`
` = - e^(x) cosec " " x`+ C (C constant of integration)