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Repeating integration by parts on eˣ sin x brings back the original integral. The final value is
Aeˣ(sin x − cos x) + C
Beˣ(sin x − cos x)/2 + C
Ceˣ(cos x − sin x)/2 + C
Deˣ(sin x + cos x)/2 + C
Answer & Solution
Correct answer: B. eˣ(sin x − cos x)/2 + C
Two rounds of integration by parts return the same integral, and solving for it gives eˣ(sin x − cos x)/2.
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