∫eˣ cos x dx equals:
∫eˣ cos x dx equals:
- A. (eˣ/2)(sin x + cos x) + C
- B. eˣ sin x + C
- C. eˣ cos x + C
- D. (eˣ/2)(sin x − cos x) + C
Answer: A) (eˣ/2)(sin x + cos x) + C
Explanation: Apply integration by parts twice. Let I = ∫eˣ cos x dx. After first parts: I = eˣ sin x − ∫eˣ sin x dx. Second parts on ∫eˣ sin x dx yields I = eˣ sin x + eˣ cos x − I. 2I = eˣ(sin x + cos x). I = (eˣ/2)(sin x + cos x) + C.
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