Indefinite Integration: Integration by parts twice MCQ

Solve this quality-checked JEE multiple-choice question, then review the correct answer and explanation.

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Integration by parts twiceHardQuestion 330011

Question

∫eˣ sin x dx equals:

A
eˣ(sin x − cos x)/2 + C
Correct
B
eˣ sin x + C
C
eˣ cos x + C
D
−eˣ cos x + C

Correct answer

eˣ(sin x − cos x)/2 + C

Explanation

Let I = ∫eˣ sin x dx. By parts twice: I = eˣ sin x − ∫eˣ cos x dx = eˣ sin x − (eˣ cos x + ∫eˣ sin x dx) = eˣ(sin x − cos x) − I. 2I = eˣ(sin x − cos x) + C → I = eˣ(sin x − cos x)/2 + C.

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