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Question
`int "e"^x (cosx - sinx)"d"x` is equal to ______.
Options
`"e"^x cos x + "C"`
`"e"^x sin x + "C"`
`-"e"^x cos x + "C"`
`-"e"^x sin x + "C"`
Solution
`int "e"^x (cosx - sinx)"d"x` is equal to `"e"^x cos x + "C"`.
Explanation:
`int "e"^x ["f"(x) + "f"(x)]"d"x = "e"^x "f"(x) + "C"`.
Here f(x) = cosx, f'(x) = `- sin x`.
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