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Question
Integrate the following with respect to x:
`"e"^(- 3x) cos x`
Solution
`int "e"^("a"x) cos "b"x "d"x = "e"^("a"x)/("a"^2 + "b"^2) ["a" cos "b"x + "b" sin "b"x] + "c"`
Here a = – 3, b = 1
`int "e"^(- 3x) cos x "d"x = "e"^(- 3x)/((- 3)^2 + 1^2) [- 3 cos x + 1 sin x] + "c"`
`int "e"^(- 3x) cos x "d"x = "e"^(- 3x)/(9 + 1) [sin x - 3 cos x] + "c"`
`int "e"^(- 3x) cos x "d"x = "e"^(- 3x)/10 [sin x - 3 cos x] + "c"`
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