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Evaluate : int e^(x) cos^(2) x (cos x-3 ...

Evaluate : `int e^(x) cos^(2) x (cos x-3 sin x ) dx`

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`int e^(x) cos^(2) x (cos x- 3 sin x) dx`
` =inte^(x). cos^(3) x dx - int e^(x). 3 cos^(2) x sin x dx`
` = cos^(3) x int e^(x) dx - int {((d)/(dx) . cos^(3) x) int e^(x) dx } dx`=
`-int e^(x) . 3 cos^(2) x sin x dx`
`=e^(x). cos^(3) x- int 3cos^(2) x (-sin x).e^(x) dx`
` - int e^(x) . 3cos^(2) x sin x dx +c`
` =e^(x) cos^(3) x + int 3 cos^(2) x sin x e^(x) dx`
` - int 3 cos^(2) x sin xe^(x) dx + c`
` =e^(x) cos^(3) x+c.`
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