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प्रश्न
Integrate the following with respect to x:
`"e"^(-x) cos 2x`
उत्तर
`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 = – 1, b = 2
`int "e"^(-x) cos "d"x = "e"^(-x)/((- 2)^2 + 2^2) [- 1 cos 2x + 2 sin 2x] + "c"`
= `"e"^(-x)/(1 + 4) [ - cos 2x + 2 sin 2x] + "c"`
`int "e"^(-x) cos "d"x = "e"^(- x)/5 [2 sin 2x - cos 2x] + "c"`
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