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